In a blender, place egg yolks, mustard, salt, sugar, white pepper, cayenne pepper, and corn starch and pulse to combine.
Add vinegar and lemon juice and blend until smooth.
With blender running, drizzle in both oils and blend until smooth. Add all the heavy cream and blend until smooth.
Bring a saucepan half full of water to a boil. Pour salad dressing into a metal or glass bowl larger than the opening of the saucepan.
Place the bowl over the boiling water and whisk vigorously while it heats and thickens, about five minutes.Remove from heat and cool to room temperature.