Toss tomatoes and 1 tsp of salt together in a second bowl. Transfer tomatoes to a colander and set colander in the sink. Let tomatoes drain for 30 minutes.
Preheat oven to 375 degrees (or 350 convection oven). Line a rimmed baking sheet with parchment paper. Take chilled dough out of refrigerator and let sit on counter for 10 minutes to soften slightly before rolling.
Roll out dough on a lightly floured surface, into a 12-inch circle. Gently roll dough over the rolling pin and transfer to prepared baking sheet. (Its ok if dough runs over the lip a bit).
Shake colander well to rid tomatoes of excess juice. Add shallots, oil, garlic, thyme, 1/2 tsp salt and pepper into the bowl and mix with tomatoes.
Spread or brush dijon mustard over the dough leaving a 1-1/2 inch border. Sprinkle the gruyere in an even layer over the mustard. Shingle the tomatoes and shallots on top of gruyere in overlapping concentric circles, keeping within the 1-1/2 inch border. Sprinkle parmesan over the tomato mixture.
Carefully grasp 1 edge of dough and fold it up over filling. Repeat around the circumference of the tart overlapping the dough every 2 inches, gently pinching the pleated dough together to secure. Brush the folded dough edge with egg (you wont need it all).
Bake until crust is golden brown and tomatoes are bubbling, about 45-50 minutes. Transfer baking sheet to a wire rack and let galette cool for about 10 minutes. Using a metal spatula, loosen galette from parchment and carefully slide onto wire rack. Let cool until just warm, about 20 minutes. Sprinkle with basil. Cut into wedges and serve warm.
Enjoy!