Preheat the oven to 425˚F (220˚C). If the dough has been in the fridge overnight (or longer), take it out so that it can start to soften (it’s best to roll it out when it’s cool to the touch, but pliable).
In a bowl, combine the softened goat cheese, garlic, and honey. Season with salt. Stir until smooth (a rubber spatula works well for this).
Sprinkle a large sheet of parchment paper lightly with flour. Roll out the dough on the parchment, lifting the dough and lightly flouring the parchment as needed to prevent sticking (if the dough starts to crack immediately it’s too cold, and, conversely, if it starts to get sticky it’s too warm). You're aiming for a 12-inch round (it should be about ⅛-inch thick). If the dough cracks, just patch it up as needed. Brush off any excess flour from the parchment paper, then slide the sheet of parchment (with the dough) onto a baking sheet. If the dough feels warm, refrigerate it for 5 minutes.
Dollop the goat cheese mixture evenly over the dough, then spread it in an even layer, leaving a 1 ½-inch border. Refrigerate the tart dough for 5 minutes. While the dough chills, cut the tomatoes into ¼-inch slices.
Arrange the tomato slices over the goat cheese layer, overlapping them as needed (you might not need all the slices). Sprinkle the tomatoes with flaky sea salt. Fold the edges of the dough up over the tomatoes, overlapping the dough and pinching it together (patch up any tears as needed). Brush the edges of the galette with melted butter or heavy cream (you won’t need it all).
Bake the galette, rotating once, until the crust is a deep golden brown, about 30-35 minutes (it takes 35 minutes in my oven—don’t underbake the galette, otherwise the crust might not crisp up on the bottom). Transfer the pan to a rack. If you see any pools of liquid on top of the tomatoes you can use a paper towel to dab them, but there’s no need to go crazy (it’s okay if there’s some liquid on top). Let the galette cool until it’s slightly warm or at room temperature (this is important, as it will set up as it cools).
Before serving, drizzle the tomatoes with chili crisp and sprinkle with chopped mint and basil. Cut the galette into slices, and serve.