Buttery Burgers and Onions on Toast

Ingredients

• 1 stick butter, divided
• 2 large onions, thinly sliced plus 1/2 small onion
• 1 tablespoon fresh thyme leaves or 1/4 teaspoon dried
• 1 bay leaf
• Salt
• pepper
• 1/2 cup beef stock
• 1 1/2 pounds 90% lean ground beef of the best quality, at room temperature
• 1 tablespoon Worcestershire sauce
• 2 cloves garlic, grated or pasted
• 2 tablespoons olive oil
• 4 slices sharp cheddar
• 4 slices Gruyère or Swiss cheese
• 1 bunch upland cress
• 8 slices (each about 3/4-inch thick) white bread