Melt the butter in a large sauté pan over medium heat, then stir in the onions. Sauté the onions until they turn a golden brown and their volume reduces by half, about 35 minutes. Add the balsamic vinegar and stir the onions with a wooden spoon to pull up the caramelized bits from the pan. Stir in the thyme, season to taste and then remove the pan from the heat and let cool at room temperature. This can be made up to a day ahead and chilled until ready to assemble.

Preheat the oven to 400°F (200°C) and line a baking sheet with parchment paper.

Lay the sheet of puff pastry on the baking sheet and dock it with a fork across the surface (this prevents it from rising too much). Spread the cooled onions in an even layer over the pastry, right to the edges, and sprinkle the crumbled bacon overtop. Arrange the cherry tomato halves overtop in 4 rows of 6. Bake the tart until it is puffed and golden brown at the edges, about 30 minutes.

To serve, transfer the baking sheet to a cooling rack for 5 minutes, then cut the pastry into 24 pieces so that a cherry tomato half is on each piece. Pick up with your fingers to eat warm or at room temperature.