Pat breasts dry with paper towels and season with salt and pepper.
Heat 1 tablespoon oil in 12-inch nonstick skillet over medium-high heat.
Add breasts and cook until well browned, about 4 minutes per side, transfer to plate (they will finish cooking in a bit in the skillet).
Add remaining 1 tablespoon oil to now-empty skillet and heat until shimmering.
Add potatoes, cut sides down, and cook until golden brown, about 7 minutes.
Stir in garlic, rosemary, oregano, and 1/2 teaspoon salt and cook until fragrant, about 30 seconds.
Add stock and wine, scraping up any browned bits, and bring to a boil.
Place breasts on top of potatoes in skillet (this will steam the chicken w/out letting them have direct contact with the hot skillet, and over cooking them).
Reduce heat to medium-low and simmer, covered, until potatoes are tender and breasts register 160 degrees, about 12 -13 minutes.
Using slotted spoon, transfer breasts and potatoes to platter and tent loosely with foil.
Increase heat to medium-high and cook, uncovered, until sauce is reduced to 1 cup, about 5 minutes.
Stir in peas and cook until heated through, about 1 minute.
Off heat, whisk in butter and lemon juice and season with salt and pepper to taste.
Pour sauce over breasts and potatoes.