Remove the fat from the chicken breasts, cut into small cubes, and pat sides dry with a paper towel.
Add butter and 2 tablespoons olive oil in a large nonstick pan over medium heat.
Chop carrots into thirds, and dice potatoes into 12 pieces each.
Place carrots and potatoes in pan with melted butter and olive oil. Allow to sauté uncovered, stirring every 3 or so minutes, for about 8 minutes.
In a large bowl, whisk together paprika, Italian seasoning, salt, pepper, and flour.
Toss chicken in spice mix to evenly coat each piece. Move the potatoes and carrots to one side of pan and add the coated chicken to the other side.
Flip the potatoes and carrots and cook for 5 minutes or until easily pierced with a fork. Stir and flip the chicken until no longer pink, the chicken will finish cooking later in the process.
Zest 1 lemon with a zester to get 1 teaspoon zest. Juice the same lemon using a citrus juicer to get 3 tablespoons lemon juice.
Add zest and juice to a small bowl with remaining 2 tablespoons olive oil and minced garlic.
Pour mixture into the pan and gently stir all the ingredients together.
Slice the remaining lemon into thin slices and add to the pan; allow the ingredients to simmer on low.
Stir the ingredients often until the liquid is absorbed, the chicken is completely cooked, and veggies are tender.
Season with lemon pepper seasoning to taste and sprinkle with fresh parsley. Discard lemon slices before serving. Serve immediately.
