Cut butter into small cubes. Add flours, salt and baking powder to a medium mixing bowl, and whisk to combine. Using a pastry blender, cut butter into the flour mixture until the largest pieces are the size of peas.
Stir in water until dough holds together. Pat dough into a disk and wrap tightly in plastic. Chill until firm, at least 2 hours.
Sauté onion in olive oil, season with salt and pepper. Set aside to cool.
Unwrap dough and roll out, on a lightly floured surface, to roughly 1/8" thick.
Gently roll up dough onto the rolling pin and place inside of the tart pan. Carefully press down along the bottom and sides, making sure to press into every groove.
Roll the rolling pin over top of tart pan to evenly "cut" dough across the top.
With a fork, dock the surface of the bottom of the dough.
Place dough in the freezer for 15 - 20 minutes (or refrigerate overnight, wrapped in plastic wrap) to allow the butter to harden before blind baking.
Cover dough with a piece of parchment paper (or foil), then place dried beans or pie weights inside. Make sure the weights go all the way to the edges of the pan.
Place tart pan on a baking sheet, and bake at 350°F / 180°C degrees for 15 - 18 minutes. Remove weights and parchment, and put back in the oven for another 4 - 6 minutes or until light golden brown.
While crust is blind baking, mix goat cheese, thyme leaves, salt and pepper (to taste) together in a small bowl.
Remove crust from oven and let it cool slightly before spreading the goat cheese mixture on the bottom of the tart crust.
Scatter onions over the layer of goat cheese.
Shingle tomato slices around edge of tart, place grape tomatoes in the middle, cut side up. Season again with salt and pepper.
Sprinkle Parmesan cheese on top.
Bake at 400°F / 200°C degrees until cheese is browned and bubbly, about 20 minutes, rotating halfway through if necessary.