Arrange slices on a large baking sheet and bake in oven until golden, about 6-8 minutes. Let cool.
Meanwhile, heat butter and oil in a 10-inch heavy skillet over medium heat until butter is melted, then cook onion, garlic, bay leaf, and thyme with 1/2 teaspoon salt and 1/4 teaspoon pepper, covered, stirring occasionally, 10 minutes.
Uncover skillet and cook, stirring occasionally, until deep golden, about 10 to 15 minutes more. Add wine and cook until entirely evaporated, 1 to 2 minutes. Discard garlic clove, bay leaf, and thyme. Transfer to a small bowl and keep warm, covered.
Arrange toasts on a large baking sheet, then top each with a rounded teaspoon of caramelized onions and sprinkle generously with shredded Gruyere. Broil 3- to 4-inches from heat until cheese is melted, 1 to 2 minutes (watch carefully).
Steps that can be done ahead of time:
Onions can be caramelized 3-5 days ahead and kept chilled.
Bread slices can be toasted and cheese shredded 1-2 days ahead. Keep toasts in an airtight container at room temperature and keep cheese chilled.