Dice the potatoes into 1/2-inch cubes and place them in a large bowl. Add the olive oil, garlic powder, smoked paprika, salt, and dried thyme, then toss until the potatoes are evenly coated with the seasoning mixture. Transfer to an air fryer basket in a single layer and air fry at 385°F for 20-25 minutes, shaking the basket halfway through to ensure even cooking. The potatoes should be golden and crispy on the edges while tender inside when done.
While the potatoes cook, cut the chicken breasts into 1-inch bite-sized pieces and place them in a bowl. In a small bowl, combine the smoked paprika, onion powder, mustard powder, dried parsley, light brown sugar, salt, adobo seasoning, and cracked black pepper. Toss the chicken with this seasoning mixture until all pieces are evenly coated. I like to let the seasoned chicken sit for a few minutes while I prepare the skillet—this helps the flavors penetrate the meat.
Heat the olive oil in a large skillet over medium-high heat. Once hot, add the seasoned chicken and cook for 3-4 minutes per side until the pieces are golden brown and reach an internal temperature of 165°F. Stir in the tomato paste and cook for about 30 seconds to caramelize it slightly, then add the BBQ sauce and stir to combine. Simmer for 1-2 minutes to let the flavors meld together. The sauce should coat the chicken nicely.
Add the cooked potatoes from Step 1 to the skillet with the chicken and sauce, gently folding them together to distribute evenly. Immediately top the entire mixture with the freshly shredded mozzarella cheese, covering it as completely as possible. Transfer the skillet to a preheated 385°F oven and bake for 5-10 minutes until the cheese is melted and lightly bubbly. I find that freshly shredded cheese melts more evenly than pre-shredded, giving you a creamier finish.