Preheat your oven to 375°F. Pat chicken dry and season generously with salt and pepper on both sides. Heat 2 tbsp butter in a large Dutch oven over medium-high heat until foaming.
Working in batches, brown chicken pieces 3-4 minutes per side without crowding the pan. Transfer to a plate once golden, then set aside for later use.
Reduce heat to medium and add remaining 2 tbsp butter to the pan. Sauté diced onion 5-6 minutes until translucent, then add minced garlic and cook 1 minute until fragrant.
Sprinkle flour over aromatics and stir constantly 2 minutes to create a paste base. Pour in chicken broth slowly while whisking to prevent lumps from forming in the creamy hearty chicken pot pie filling.
Return chicken to the pot along with potatoes, frozen vegetables, thyme, and rosemary. Bring to a simmer, then reduce heat to low and cook 15-18 minutes until potatoes soften partially.
Stir in heavy cream and adjust seasoning with additional salt and pepper as needed. Transfer the entire mixture to a 9x13 baking dish.
For the topping, whisk flour, baking powder, and salt together in a bowl. Cut cold butter into small cubes and work into the flour mixture using a fork until breadcrumb texture forms.
Add milk and stir gently just until combined—don't overmix. Drop spoonfuls over the filling, leaving small gaps for steam. Bake 22-25 minutes until golden brown and cooked through completely.