Japanese Egg Salad Sandwich (Tamago Sando)

Place eggs in the bottom of a saucepan. Add 1/4 inch of water. Heat over medium-high heat and bring to a boil. Cover and steam for 11 minutes. Turn off the heat and drain water carefully; pour cold water over and let cool. Mix mayonnaise, salt, sugar, mustard, hot sauce, lemon juice, and vinegar for Kewpie-style mayonnaise together. Cover with plastic wrap and refrigerate until needed. Peel eggs. Mash in a shallow bowl with the side and back of a fork until desired texture is reached. Add salt, sugar, cayenne, heavy cream, and 3 tablespoons Kewpie-style mayonnaise. Stir to combine. Wrap and refrigerate until well chilled, at least 1 hour. Taste and adjust seasonings. Butter bread slices and use 1/2 of the egg salad on each sandwich. Cut crusts off before serving if you're fancy.