To make the salsa Verde, arrange the tomatillos, red onion, poblano, jalapeno, and garlic onto a baking sheet. Add salt and olive oil and toss to combine.
Roast the tomatillo mixture for 15-20 minutes until the vegetables have softened.
Carefully place the roasted vegetables into a food processor. Add the lime juice and cilantro, and blend until pureed.
To make the chicken, season them generously with salt and pepper.
Place the all-purpose flour into a shallow dish and dredge both sides of the chicken in the flour, shaking off any excess flour.
Place the butter into a large, heavy-bottom pot and set it over medium-high heat.
Once the butter melts, add the chicken and cook it for 3-4 minutes. Turn the chicken over and cook it for an additional 3-4 minutes until golden brown.
Place the chicken breast onto a plate and set it aside.
Add chicken broth to the pot and run your spoon along the bottom of the pot to release any browned bits.
Add the salsa Verde, garlic, cilantro, and cumin to the chicken broth and let it come to a boil.
Decrease the flame to medium-low and return the chicken breast to the skillet. Add the lime juice. Spoon the salsa Verde sauce over the chicken to coat it in the sauce.
Cook the Pollo en salsa Verde for 15 minutes until the chicken has a temperature of 165°F.
To serve, place the chicken breasts onto a serving platter and add the salsa verde sauce. Add the sour cream and green onions.
Serve and enjoy!