Place a large skillet over medium-high heat. Add 1/4 cup of butter and melt.
Add onion, garlic, mushrooms, and bell pepper, and saute while stirring occasionally, until just tender, for about 4-5 minutes. Transfer mixture to a plate and set aside.
Reduce heat to medium-low. Add the remaining 1/4 cup of butter and melt.
Whisk in flour, salt, and pepper. Stir constantly, until smooth, for about 1 minute.
Little by little, whisk in milk and after that chicken broth, if the mixture is too thick, add more broth. Bring to a low simmer, stir and cook for 4-5 minutes. If needed, stir in more chicken broth.
Stir in the cooked veggies and chicken, also add the frozen peas and diced pimientos. Stir well, so everything is coated in the sauce, and cook until chicken is warmed through. Add more broth if the sauce is too thick. Taste and adjust for salt and pepper.