Preheat the oven to 375 degrees F.
Roll the pastry dough out to a flat even layer. Place into a 9-inch tart pan with a removable bottom, letting 1 to 2 inches of dough fall over the sides of the pan. Set the tart pan on a baking sheet.
In a large bowl, whisk together the milk, cheese, thyme and eggs. Season the mixture lightly with salt and pepper. Stir half of the squash blossom petals into the egg mixture.
Pour the egg mixture into the tart pan lined with the dough. Place the remaining squash blossom petals on top of the egg mixture. Gently fold the edges of the dough over the egg mixture. (Leave some space between the eggs and dough, as the eggs will souffle in the oven and will need space to rise.)
Bake until the eggs have puffed and the crust is golden brown, about 20 minutes.