RIP to the best yum-yum sauce recipe I have found, https://japanese-steakhouse-white-sauce.com/home/ (working wayback machine link). In its honor I'm posting the recipe here, along with my family's modifications.
OG recipe:
- Mayonnaise (Hellman's), 1-1/4 cup
- Water, 1/4 cup
- Tomato paste, 1 teaspoon
- Melted butter, 1 tablespoon
- Garlic powder, 1/2 teaspoon
- Sugar, 1 teaspoon
- Paprika, 1/4 teaspoon
- Cayenne pepper, dash
You can just mix everything together in this version, no particular order. The author stresses that it won't taste right if you use a different brand of mayo. He says it makes it taste too strongly of mayo. He particularly cautions the use of low fat or reduced calorie mayo, and the substitution of ketchup for the tomato paste. Once mixed the sauce should be refrigerated immediately and allowed to chill overnight for best results. Best within 7-10 days.
OG "from scratch":
- Soybean oil, 3/4 cup
- Egg, 1
- Dry mustard powder, 1/2 teaspoon
- Salt, 1/2 teaspoon
- Sugar, 2 teaspoon
- Cayenne pepper, dash
- White vinegar, 1-1/2 tablespoons
- Cayenne pepper, dash (duplicate line is reflective of his recipe. It's unclear if this is a typo or he adds it twice in different stages, although the written instructions don't indicate that.)
- Tomato paste, 1-1/2 teaspoons
- Melted butter, 1 tablespoon
- Garlic powder, 1/2 teaspoon
- Paprika, 1/4 teaspoon
- Water, 1/4 cup
Copypasta instructions:
Set up blender. Put 1/4 cup (only) of the oil along with the egg, vinegar, mustard powder, salt, cayenne and 1 teaspoon of the sugar in the blender and place the lid on the blender. Turn it on and let everything mix well for about 5-10 seconds. Turn off the blender.
Open the pouring hole in the blender lid or take off the small removable center piece. Turn the blender back on, and very slowly drizzle the remaining 1/2 cup oil through the hole into the mixture while it is blending. It should take 30 seconds or so – if not, you are pouring too fast!
*** If you add the oil too fast, it will not emulsify (come together) properly, and will not be the consistency of mayo – it will be more like white oil and you will need to throw it away! ***
Once the mixture has emulsified, turn off the blender. Empty the contents into a mixing bowl. Using a fork or a whisk, mix in the remaining 1 teaspoon sugar along with the tomato paste, melted butter, garlic powder and paprika. Mix throughly until the sauce is smooth. If it is too thick, add some of the water (up to 1/4 cup) to get it to the desired consistency. Refrigerate overnight to allow flavors to blend. Bring to room temperature before serving.
And finally, my family's take! Our changes deepen the flavor a bit and increase the kick. Note that this recipe is based on a double portion. YMMV trying to make more or less, I've found that the proportions don't always scale properly. We typically use Duke's mayo, just because it's what we keep in the fridge. I suggest starting with 2 cups of mayo and the water, mixing, and slowly adding mayo until you reach your preferred consistency. We tend to make it pretty thick because we mix it into white rice.
- mayo, 2 - 2.5 cups
- water, 1/2 cup
- tomato paste, 3 tsp
- melted butter, 2 tbs
- garlic powder, 1.25 tsp
- sugar, 2 tsp
- paprika, 1.5 tsp
- cayenne, .5 tsp
- OPTIONAL mirin or rice wine vinegar to taste
- vinegar adds tang
- mirin adds smoothness
One thing that will definitely not work for most people here is the emulsification. It can't be done reliably in a regular blender with a regular blending vessel.
Emulsification needs a space constraint by volume to ensure the cycling of ingredients to quickly bind and stabilize. A wide mouth jar and immersion blender will be a much better choice for this volume. You also need to make sure that when you start blending anything for emulsion, the solids need to be settled to the bottom of the vessel before blending, so slowly adding oil is somewhat unreliable as well. Add your solids, slowly pour your liquids in order on top (oil before water for example), THEN blend as fast as possible.
The order when this happens is: proteins > heavy liquids and solids mix > medium liquids bind > light liquids bind as far as ingredients go. As long as you have a setup where this is ensured, it's almost guaranteed to work every time.
Adding anything individually will not reliably work, and will make a "loose" emulsification as you mentioned.
I can't speak to any of this, I've never attempted the from scratch version. I copied the recipe and instructions just to preserve them.