Add 1 tsp. of olive oil to a large skillet over medium heat.
Season the chicken breasts with salt and pepper, then add them to the skillet. Sauté for 3 minutes on each side or until golden brown and almost cooked through, then set aside.
In the same hot skillet, add the remaining tsp. olive oil and lower heat.
Add garlic and allow to cook for about 30 seconds.
Add green onion and half of the broth. Raise the heat to medium.
Add mushrooms & peppers, bringing everything to a medium simmer. Cook for 5 minutes.
In a separate bowl, whisk together the yogurt, cashew milk, and 1 tsp. parsley, then pour into the skillet.
Add spinach and stir until combined.
Allow sauce to bubble lightly with vegetables, lowering heat if needed and stirring occasionally, for 5 more minutes.
Nestle chicken breasts into the skillet. Add remaining broth and mascarpone or cream cheese, then cook for 5-10 more minutes until chicken is cooked through and the sauce has thickened.
Season with salt and pepper, top with remaining parsley, and serve.