Slice tomatoes about ⅛ inch thick then arrange on a double layer of paper towels. Press a double layer of paper towels over top to soak up excess liquid. Set aside while you prepare remaining ingredients.
Heat oven to 400ºF (204ºC) with rack set in middle position. Line two baking sheets with parchment paper.
Unfold puff pastry and using a 3 ¼-inch round cookie cutter, cut out 2 rounds; transfer to baking sheets.
Spread 2 teaspoons goat cheese onto each round, leaving an ⅛-inch boarder around edge of dough.
Arrange two slices of shallot over goat cheese. Place 1 slice of tomato on each tart dough and sprinkle with fresh thyme.
In a small bow, beat egg and a splash of water until smooth. Using a pastry brush, brush edges of puff pastry dough with egg wash.
Transfer baking sheets to oven and bake until puffed and golden brown around the edges, about 25 minutes, rotating top to bottom and front to back halfway through.
Meanwhile, combine honey and chili crisp in a small bowl; add a splash of water to thin the sauce.
Drizzle honey sauce over tarts and sprinkle with flaky sea salt; serve immediately.