Use paper towels to pat the chicken breasts dry. Season them with 1/8 teaspoon of salt and 1/8 teaspoon of pepper.
COOK THE CHICKEN:
Preheat a 12-inch skillet over medium-high heat with 2 teaspoons of canola oil in it. Place the chicken in the hot pan and cook for about 5 minutes, or until the bottom is golden brown. Flip the chicken over and keep cooking for 3 minutes. Move the chicken to a plate.
COOK THE POTATOES:
Over medium heat, add the remaining 2 teaspoons of canola oil to the skillet. Place the potatoes, cut side down, in the pan and cook for about 7 minutes, or until golden brown. WIth the potatoes still in the pan, add the garlic, oregano, and rosemary to the skillet and cook until fragrant, about 60 seconds.
Add the flour and cook, while stirring constantly, for 1 minute. Slowly pour in the broth and wine while scraping up any browned bits from the bottom of the pan; bring the mixture to a simmer.
COOK THE CHICKEN AND POTATOES:
Nestle the chicken into the skillet and cover. Cook over medium-low heat until the chicken reaches 165 degrees F on an instant-read thermometer and the potatoes are fork-tender, about 12-14 minutes. Use a slotted spoon to move the chicken and potatoes to a platter, and cover with foil.
MAKE THE SAUCE AND COOK THE PEAS:
Crank the heat up to medium-high and cook the sauce until it is reduced to 1 cup, about 3-5 minutes. Add the peas and stir until the peas are heated through, about 1 minute. Take the skillet off of the heat and whisk in the butter, lemon juice, and lemon zest. Season to taste with salt and pepper. Spoon the sauce and peas over the chicken and potatoes and serve right away.