Put the whole shallots onto a sheet of aluminum foil. Cut the pointed top off the garlic bulb and put it next to the shallots. Add the thyme sprigs, drizzle everything with the olive oil and season with salt and pepper. Fold up into a loose package and bake until soft, 35 to 40 minutes. Remove from the oven, open the package and set aside to cool.
Mix the ricotta with the truffle oil. Set aside.
Squeeze the shallots and garlic out of their skins and onto a board. Chop very finely and add to a bowl with the softened butter. Season with salt and pepper and mix well. Refrigerate the compound butter until you are ready to use it. You can also roll it up into a cylinder in plastic wrap and freeze it for up to 3 months.
Sprinkle the beef, pork and veal with salt and pepper. Mix well and form into 4 thick patties. Set aside.
When you are ready, melt 2 tablespoons of the compound butter in a medium nonstick skillet over medium heat and add the meatballs. Fry until they are cooked through, an internal temperature of 160 degrees F. Remove from the skillet, cover and keep warm.
Add the pate slices to the skillet and cook until lightly browned on both sides, about 20 seconds per side. Remove from the skillet and keep warm.
Build the burger: Butter a warm slice of brioche toast with some compound butter and put it onto a plate. Top with a meatball and a slice of pate. Spoon a big dollop of the truffled ricotta on top and garnish with the sprouts. Serve immediately.