Toss tomatoes and 1 tsp salt together. Transfer tomatoes to a colander and let drain for 30-45 minutes. Transfer again to a salad spinner and spin briefly to remove more liquid.
While tomatoes drain, roll dough into a 12" circle then transfer to a parchment lined baking sheet.
In a large bowl, combine tomatoes, shallot, oil, thyme, garliic, pepper and ½ tsp salt.
Spread mustard over dough, leaving a 1½" border. Sprinkle cheese over mustard. Shingle tomatoes in concentric circles over cheese. Sprinkle parmesan over tomatoes. Fold up edges of dough to cover edge of filling. Brush folded dough with egg. Bake until crust is golden brown and tomatoes are bubbling, 45-50 minutes.
Transfer to a wire rack to cool for 10 minutes. Transfer to serving dish and allow to cool for 20 minutes; sprinkle with basil and cut into wedges for serving.