Preheat the oven to 425 degrees F.
Heat 1 tablespoon of the oil in an extra-large nonstick ovenproof skillet over medium-high heat. Add the garlic and onion and cook, stirring, until the onion is softened and lightly browned, about 3 minutes. Add the artichokes and cook until warmed through, about 1 minute. Add the spinach and cook, stirring, until completely wilted, about 3 minutes. Transfer the mixture to a medium bowl and let cool completely. Wipe out the skillet and reserve.
When the spinach mixture is cool, add the mayonnaise, lemon zest and 7 tablespoons of the cream cheese spread and stir to combine. Season with salt and pepper.
Insert a thin paring knife into the thickest part of each chicken breast and cut down the side to make a 3-inch-long pocket. Stuff each pocket with one-quarter of the spinach mixture. Sprinkle the chicken with salt and pepper.
Return the skillet to medium-high heat and add the remaining 1 tablespoon oil. Add the chicken breasts skin-side down and cook until golden brown, about 4 minutes; transfer to a plate. Add the potatoes to the skillet, sprinkle with salt and pepper and cook, tossing, about 2 minutes. Turn off the heat, return the chicken to the skillet skin-side up and transfer to the oven. Roast, stirring the potatoes halfway through, until an instant-read thermometer inserted in the thickest part of the chicken registers 165 degrees F, 25 to 30 minutes.
Meanwhile, combine the roasted peppers, lemon juice and remaining 3 tablespoons cream cheese in a food processor or blender and process until smooth. Season with salt and pepper.
Spoon the red pepper sauce onto 4 plates. Top each with a chicken breast and some potatoes.
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