Make the crust: Freeze cubed butter for 20 minutes. In a food processor, pulse the flour and sea salt until incorporated. Add the cold butter and pulse until just pea-size pieces of butter remain, 15 to 20 pulses. Add the ice water and pulse until a dough just forms, 15 to 20 pulses.

Turn the dough out onto flour-dusted work surface gather into two 5-inch discs. Wrap in plastic wrap. Freeze one of the discs for another use (it will last for weeks in the freezer if you wrapped it nice and tight). Chill the other dough disc in the refrigerator for at least 30 minutes (or up to 2 days).

Preheat the oven to 375°F.

Place the dough on a piece of parchment paper. Using a floured rolling pin, roll the disc into a 12-inch round (it doesnt have to be perfect). Prick it all over with a fork. Put the dough, with the parchment, on a baking sheet and bake until golden and crisp, about 30 minutes. (Try cutting dough before baking into rounds or squares). Cool thoroughly and break into pieces.

Make the soup: In a 4 cup measuring cup microwave the milk and 2 cups of broth until simmering. set aside

Meanwhile, in a big soup pot, heat the butter over medium-high heat until foamy. Add the garlic and cook, stirring, until fragrant, about 1 minute. Add the flour, reduce the heat to medium, and cook, stirring, until toasty and foaming, 2 to 3 minutes. Whisk in the broth-milk mixture, slowly at first.

Bring to a boil, then reduce the heat and cook until thickened, about 5 minutes. Add the potato, carrots, peas, pearl onions, and ham and simmer until the potatoes are tender, about 20 minutes. Add the salt and pepper to taste

Stir in the chicken and cream and heat through for 5 additional minutes. Season with salt and pepper to taste and serve with the broken pie crust on the side.