Make the onions: Set the multicooker to high saute. Add the butter and olive oil, and let the butter melt. Stir in the yellow and red onions. Cook, stirring occasionally, for about 5 minutes, or until softened. Stir in the sherry, thyme, bay leaves, salt, and pepper.

Place the lid on the multicooker, and lock it. Set the valve to the Sealing position. Cook on high pressure for 15 minutes. Quick-release the steam.

Remove the lid from the multicooker, and set to high saute. Remove the bay leaves. Cook, stirring often, for about 10 minutes, or until the onions are jammy and golden brown and most of the liquid is reduced. Pour in the beef stock, and stir to scrape up the browned bits in the bottom of the cooker insert (this is called deglazing). Stir in the balsamic vinegar. Taste and adjust seasoning with more salt if needed.

Make the sandwiches: Spread 1 tablespoon mayonnaise on 1 slice of each slice of bread. On 4 of the bread slices (mayonnaise-side facing out), layer ⅓ cup grated Gruyère, 2–3 tablespoons of the caramelized onion mixture, and ⅓ cup shredded mozzarella. Top each with a second slice of bread, mayonnaise-side facing out.

Melt 3 tablespoons butter in a skillet over medium-low. Place 1 sandwich in the skillet, and cook until the bread is golden and crispy, 3–4 minutes per side, pressing gently with a spatula, and reducing the heat if needed if the bread starts to overbrown. Repeat the process with the remaining butter and 3 sandwiches.

Slice the sandwiches in half, and serve while the cheese is hot and gooey.