In a medium pot, set over medium heat, add the olive oil. When the oil is warm, add the shallot, diced carrot and squash; cook until the shallot is translucent and carrot and squash have softened slightly, about 3 to 5 minutes. Mix in the minced garlic, thyme leaves and butter.
Stir until butter is melted and then add the flour. Cook for 1 to 2 minutes longer and then pour in the chicken stock. Bring the mixture to a simmer and then immediately turn the heat to low. Give it a try—you’ll definitely need salt! Add salt to taste (I added about 1 teaspoon) and add a few rounds of pepper. I found the more pepper, the better. The filling should be the texture between a broth and a gravy; thickened but not too thick. Take it off the heat and let it sit while you roll out the crust for the pot pies.
Remove the first round of dough from the fridge. Liberally flour your work surface and rolling pin. We’re going to start by making the tops. Begin to roll the dough, being sure to rotate it every so often, to avoid sticking. Place your Le Creuset cocotte face down on top of the dough, so you can get an idea of how big the circumference of the top should be. Using a paring knife, cut out three circles, leaving a 1-inch overhang. Remove the second round of dough from the fridge and roll it out. Press the dough onto the bottoms of cocottes and up the sides. If you like, you can use the extra dough to make a lattice or cut out little leaves—the possibilities are endless for the tops.
Divide the filling amongst the cocottes and place the dough tops on. Tuck the edges under and then crimp them all the way around. Brush the dough with egg wash and transfer to the freezer to chill for 15 minutes.
Preheat the oven to 350 degrees F and bake for 45 to 50 minutes, until the tops are golden brown. Remove from the oven and let stand for 5 minutes (they’ll be super hot!). Eat immediately.
*If you're going to make your own pie-crust for this recipe, just be sure to leave out the tablespoon of sugar!