Dry the chicken breasts with a paper towel, then season with salt and pepper. In a large, non-stick skillet over medium-high heat, heat 1 tablespoon of oil until just smoking. Cook the chicken until golden brown on both sides, about 5 minutes, flipping halfway through. Transfer the chicken to a plate and keep warm.
In the same skillet, heat the remaining 1 tablespoon of oil over medium heat until shimmering. Add potatoes to the skillet, cut side down, and cook until golden brown, about 7 minutes.
Stir in the garlic, rosemary, oregano, and 1/2 teaspoon of salt, and cook until fragrant, about 30 seconds. Stir in the broth and deglaze the pan with the wine, scraping up any brown bits on the bottom of the pan.
Return the chicken to the pan, along with any juices. Bring to a simmer and cook, uncovered, until the thickest part of the chicken breast is done (165 degrees on an internal thermometer). Transfer the chicken and the potatoes to a serving dish and tent with foil.
Increase the heat to medium-high and cook the sauce until it reduces to about 1 cup, approximately 5 minutes. Stir in the peas and cook until heated, about 1 minute.
Turn off the heat and whisk in the butter and the lemon juice, and season with salt and pepper to taste. Pour the sauce over the chicken and potatoes and serve.