To make dough, in the bowl of your food processor, pulse flour, sugar, and salt to combine. Pulse in butter, until dough has a slightly sandy texture. Drizzle in water, pulsing just until it is well-dispersed in dough.

Dump out onto a lightly floured surface and gather into a ball. Flatten into a disc, wrap in plastic wrap, and chill at least 30 minutes.

Preheat oven to 400 degrees F. Place a rimmed baking sheet (one big enough to accommodate your tart pan) in oven to heat as well. Grease a 9 or 10-inch tart pan and set aside.

Toss all of filling ingredients together in a small bowl. Set aside and allow ingredients to mingle while you roll out crust.

On a lightly-floured surface, roll tart dough out into a 12-inch circle. Fold into quarters, then unfold in the tart pan. Tuck any overhanging dough into sides of tart. Scatter blackberries and any juice; place on heated baking sheet and into oven immediately. Bake about 30 minutes, or until crust is a very light golden and berries are bubbling.

Cool 20 minutes, slice, and serve.