Pulse flour and salt in a food processor until mixed. Add butter and pulse 10-12 times until butter is the size of peas. Drizzle water over flour and pulse until dough forms moist crumbs and is starting to bind together, about 8-9 pulses.

Turn dough onto a large piece of plastic wrap. Using your hands, shape the dough into a 4-inch square and wrap tightly with plastic, and refrigerate for at least 2 hours, and up to 24 hours.

Heat 2 tbsp. olive oil in a large pot over medium-high heat. Generously salt and pepper chicken, then add to the pot and cook until brown, 7-8 minutes. Transfer chicken to a large bowl.

Reduce heat to medium and add 2 tbsp. olive oil to same pot and add the onions and carrots. Cook, stirring occasionally, until veggies are starting to soften, about 8-10 minutes. Add the garlic, and stir constantly until fragrant, about 30 more seconds. Scrape the veggies into the bowl of chicken.

Position a rack in the center of the oven, then preheat to 425 degrees, and remove the dough from the refrigerator.

Melt butter in same pot over low heat. Add the flour and cook, whisking constantly, until flour and butter are incorporated. Slowly whisk in chicken broth and milk, adding a little at a time, and whisking until well mixed after each addition. Whisk all of the clumps out, until you have a smooth texture. Bring to a boil, then add chicken and veggie mixture, potatoes, and corn. Add a generous pinch of salt and pepper. Reduce heat to medium and simmer gently, stirring occasionally until the potatoes and carrots are tender, 15-18 minutes. Stir in peas and thyme.

Turn dough onto a lightly floured surface and roll the dough into a 1/8" thick rectangle. Place a ramekin or bowl face down onto the dough as a stencil, then use a knife to cut out a circle in the dough, which will be slightly larger than the diameter of the ramekin or bowl. Repeat until you have 6 dough circles. Cut one small X in the center of each circle.

Distribute filling evenly among six ovenproof bowls or ramekins that are 2-3" deep and hold at least 2 cups.

Top each bowl of stew with a dough circle. Using your fingertips, gently press the dough down into the edge of the stew.

Place pot pies on a foil-lined rimmed baking sheet (this is important, because it will most likely boil over, and you don't want a stinky mess in your oven). Bake until the filling is bubbling and the crust is deep golden-brown, about 30-35 minutes. Cool on a rack 20-30 minutes before serving (if you can wait that long!)