Center a rack in the oven and preheat to 410 (F).
In a Pyrex type oven-safe bowl, combine 6 tablespoons unsalted butter, 3 tablespoons water, 1 tablespoon granulated sugar, 1 tablespoon vegetable oil, and a pinch of salt.
This is going to sound weird, but place the bowl in the preheated oven for 15 minutes, until the mixture is boiling and the butter starts browning.
After 15 minutes, remove from the oven, and add 5.5 ounces of flour quickly, by spooning in flour in 1 tablespoon sized chunks. Use a heatproof rubber spatula to stir in the flour until it pulls off the sides of the bowl. The mixture is gonna bubble and smoke, but trust the recipe!
Once the dough is cool enough to touch, use the back of your hand to flatten out the dough onto your tart pan, using your finger tips to mold the dough up into the corners and sides of the pan. It will feel a little greasy and kinda unpleasant (the dough has the texture of mashed potatoes), but go with it. Once all the pans are lined, use a fork to poke several holes into the crust.
Place the tart pan on a baking sheet and bake at 410 (F) for 15 minutes, or until the crust is light brown and starts to appear flaky. Once it does, remove carefully from oven and let rest on a wire rack. This crust is very forgiving — it should have hardly any cracks. If you are worried about cracks, you can reserve some of the dough to press into any cracks that might appear after the baking process — the residual heat from the freshly baked tart will bake the dough accordingly and patch up your crust. Once the crust is completely cooled, it is ready for filling.