Preheat the grill with half a chimney of hot coals. Don’t put the grate back on.
Cut lobster in half with a heavy knife. Remove black intestinal tract or tomalley (green stuff) if present.
Brush the shell with some oil to make it shiny and brush the exposed meat with a mixture of melted butter, chicken rub, and lemon juice, then if you want, some minced garlic.
Use a piece of cardboard as a fan to blow away excess ash from the burning coals. Use tongs and heat-resistant gloves to lay the lobster shell side down directly in the middle of the coals Cook for about 8-12 minutes.
Baste the lobster with more of the melted butter mixture as it cooks. When done the meat should be firm and opaque all the way through. Do not overcook the lobster else it will become tough.
Foo Foo Egg Sauce
Melt the butter. It should be to the point where it is just about ready to boil.
Use an immersion blender to blend the 2 egg yolks in a small cup.
Add the lemon juice, shallot, miso paste, and a pinch of white sugar.
Use the immersion blender to combine then slowly drizzle in the hot butter while moving the immersion blender up and down to emulsify the seasoned egg foam. This is known as foo foo sauce.
Remove the cooked lobster from the coals and brush off any ash on the lobster shell.
Drizzle the foo foo egg sauce immediately over the lobster.