Broccoli Cheddar Pot Pie

Ingredients

• ***For the crust:***
• 1 cup all-purpose flour, plus more, to taste, for dusting the work surface
• 1/4 teaspoon kosher salt
• 1/3 cup salted butter, cold and diced
• 1 egg yolk, plus 1 egg, beaten, divided
• 1 tablespoon milk, plus more, to taste
• coarse sea salt, to taste
• ***For the filling:***
• 1/2 tablespoon olive oil
• 1 pound chicken breast, boneless and skinless, cubed
• kosher salt, to taste
• pepper, to taste
• 2 tablespoons butter
• 1/4 cup all-purpose flour
• 1 3/4 cups milk
• 1/4 teaspoon garlic powder
• 1/4 teaspoon onion powder
• 1 (8-ounce) package sharp cheddar cheese, shredded
• 4 cups small broccoli florets
• 2 medium carrots, sliced