Step 1In a food processor, pulse the flour and the salt, then add the butter and pulse until the butter pieces are very small, like grains of rice.
Step 2Turn out the mixture into a large bowl and sprinkle 3 tablespoons of ice water over it. Mix together gently with your fingertips. Gather the dough together into a ball, flatten it into a disc and wrap in plastic. Refrigerate for about half an hour.
Step 3Heat the oven to 425 degrees. Roll the dough out onto a floured surface, to 11 to 12 inches round, being sure not to overwork the dough. Drape the dough over a 9-inch tart pan, pressing it into the pan and removing the excess dough. Prick the bottom all over with a fork and put the dough in the freezer for about 20 minutes.
Step 4Place a piece of parchment on top of the dough and fill with pie weights. Bake for 20 minutes, then remove the parchment and pie weights. Return the tart shell to the oven and bake until the crust is golden, about 5 minutes. Remove and cool.
Step 5With a whisk or in a mixer, mix the egg, goat cheese, yogurt, salt and pepper until smooth.
Step 6Reduce the heat to 400 degrees. Gently fold 1 cup of the thyme flowers into the goat cheese mixture. Spread the mixture into the tart shell.
Step 7Bake the tart until the filling is set and just starting to turn golden on top, 25 to 30 minutes. Sprinkle the remaining 2 tablespoons thyme flowers over the top. Serve warm.