Pre-heat oven to 400 F.
To prep the tomatoes: toss the slices with a teaspoon of kosher salt and spread them on a clean dish towel or parchment lined baking sheet and let sit for at least 15 minutes. Pay them dry with paper or dish towels.
To make the mascarpone cheese filling: combine mascarpone, garlic, lemon juice, salt and pepper in the bowl of a food processor and mix until it’s all combined and smooth.
To roll out the dough: do it on a well-floured surface. Transfer dough to parchment paper lined baking sheet/tray (so that you are assembling the galette directly on what it will be baked on). Chill in freezer for 10 minutes.
To assemble the galette: spread the mascarpone mixture on the dough, leaving a 1-2’ border. Pile the tomatoes on top of the mascarpone. Fold the edges of the galette dough over the tomatoes. Brush the sides of the galette with the egg wash and sprinkle with the parmesan cheese. Drizzle tomatoes with olive oil, freshly cracked black pepper and flaky sea salt.
Transfer galette to oven and bake for 35-45 minutes, until the crust is golden brown, and tomatoes are starting to burst.
Top with basil and serve warm.