Heat the butter and olive oil in a large, deep saute pan or Dutch oven over high heat. Add the shrimp and saute over high heat, stirring occasionally until the shrimp turns pink, about 2 to 3 minutes. Remove from heat and set aside on a plate.

Season the chicken breasts with salt and pepper on both sides, reduce the heat to medium, and then place them in the pan (there should still be some butter and oil in the pan; if not, add a little more). Cook chicken over medium heat for 3 to 4 minutes on each side. Add the wine, followed by the chicken broth, shallot, and garlic; cook for another 6 to 8 minutes or until chicken is fully cooked through. Remove the chicken and set it aside on a plate.

Add the cream, mustard, lemon juice, and herbes de Provence to the pan and stir to combine. Remove pan from the heat.

Peel the shells from the shrimp. Transfer the shrimp to a bowl. Return the sauce to the heat, bring to a boil, and simmer until thickened slightly, about 2 to 3 minutes. Return the chicken and the shrimp to the pan and reheat for 1 to 2 minutes. Sprinkle in pistachios and then divide among 4 plates.