Preheat the oven to 400 degrees F. Line a baking pan with parchment paper.
Stir the mascarpone, Parmesan and egg yolk together in a bowl with a large pinch of salt and a few grinds of black pepper.
Unroll the pie crusts and cut out 8 rounds with a 4 1/2-inch round cookie cutter. Lay out the rounds on a work surface and drop a level tablespoon of the cheese mixture onto the center of each, spreading just enough to leave a 1/4-inch border. Arrange the tomatoes on top of the cheese in the center of the tarts (about 6 halves per tart), leaving about a 1/4-inch cheese border. Fold and crimp the edges of the crust just over the cheese but leaving the tomatoes uncovered. Top the tomatoes with the shallot and thyme, drizzle with the olive oil and sprinkle with a pinch of salt and pepper.
Transfer the tarts to the prepared baking pan and bake until the crust is golden brown and the tomatoes are wilted and lightly browned in spots, 20 to 25 minutes. Serve warm or at room temperature.