Mix flour and salt in a medium bowl. Add in chopped butter. Mix with a pastry cutter, two forks, or your fingers. I prefer to use my fingers, mixing in the butter by hand with the flour until you have pea-sized pieces of butter. Mix ice water and yogurt together in a small bowl. Add yogurt mixture to flour mixture. Stir to form dough. The dough will be somewhat sticky and craggily. Form into a ball and wrap in plastic wrap. Chill in the refrigerator for at least an hour. Can be made up to 24 hours a head of time.

While the dough is chilling, preheat oven to 350 degrees. Lightly grease cookie sheets. Arrange sliced tomatoes and garlic cloves in a single layer on cookie sheets. Drizzle with olive oil. Sprinkle with salt, pepper, and red pepper flakes. Bake 45 minutes, checking halfway through, turn if necessary. Your kitchen will smell amazing after about 15 minutes! Let the tomatoes cool for 15-30 minutes.

Increase oven temperature to 400 degrees. If you have a pizza stone, place it in the oven to preheat it. Roll out the chilled dough into a circle on a heavily floured surface to 1/8 inch thickness. Place half of roasted tomatoes and garlic onto the center of the dough, leaving a 2-3 inch boarder. Top with parmesan cheese and then the rest of the roasted tomatoes and garlic. Fold the edges of the dough over onto the tomatoes. Brush lightly with beaten egg. Transfer the uncooked galette onto a parchment paper lined cookie sheet or the preheated pizza stone. Bake for 40 minutes, checking halfway through. Cool on a wire rack. Serve warm, at room temperature, or chilled.