Preheat the oven: Preheat the oven to 375°F.
Cook veggies: Melt butter with olive oil in a 12” cast iron skillet or a 3.5 qt braiser (pictured) over medium-high heat. (May use a different skillet and transfer to a baking dish to bake). Add the onions, bell peppers and carrots; sauté until the onions are softened, about 5-7 minutes. Add garlic and sauté 30 seconds. Add broth: Sprinkle flour over the vegetables and cook while stirring for 2 minutes. Reduce heat to low and stir in the chicken broth, followed by the milk. Add the chicken bouillon and all seasonings.
Thicken sauce: Bring to a simmer, whisking constantly, and continue to simmer until thickened to desired consistency. The consistency now will be the same as when it comes out of the oven. For a thinner consistency, stir in additional chicken broth or milk; for a thicker consistency, simmer longer. Season to taste with salt and pepper (I add 1/2 teaspoon salt, 1/4 teaspoon pepper).
Add turkey, peas: Stir in the turkey and peas and heat through for about 1 minute over medium heat.
Top with mashed potatoes: Spread the mashed potatoes evenly over the filling, then create soft peaks with the back of a spoon. Evenly top with shredded cheese. Bake: Transfer to the oven and bake for 30 minutes or until the filling is bubbly and the cheese is completely melted. Broil for 1-2 minutes, or until the potato peaks are golden (watch closely so it doesn't burn!). Garnish with fresh parsley if desired before serving.