Pierce each potato twice, once on top and once on bottom. Microwave for 5 - 8 minutes until nearly soft, then set aside to cool slightly and cut into quarters.

Pound thicker parts of chicken to even thickness. Season with salt and pepper, then sprinkle 1 tsp rosemary and 1 tsp thyme evenly over chicken.

Melt 1 Tbsp butter in a large skillet over medium-high heat and add olive oil. Add chicken to skillet, seasoned side down, and cover with a splatter screen if available.

Cook until bottom is golden brown, about 6 minutes. Then sprinkle tops with salt and pepper and another 1 tsp each of rosemary and thyme.

Flip chicken and continue cooking until center registers 165 degrees F, about 6 minutes longer. Transfer chicken to foil, spritz with juice of half the lemon, and wrap to keep warm.

Melt remaining 1 Tbsp butter in the same skillet over medium-high heat and add olive oil. Add garlic and sauté until lightly golden, about 30 seconds, then add potatoes and remaining 1 tsp rosemary.

Cook while tossing occasionally for 3 minutes, then add green beans, seasoning veggies with salt and pepper to taste, and cook until tender, about 4 minutes longer.

Spritz with juice of remaining lemon half and return chicken to the skillet. Sprinkle with a little more rosemary and thyme, and serve immediately.