Preheat the oven to 375°F. Spray a baking dish with non-stick cooking spray or brush with olive oil. Rinse and pat dry chicken breasts. Place chicken in the baking dish, season with kosher salt and pepper, and coat with pesto (about 2 tbsp per chicken breast, depending on the size).
Bake chicken in the oven for 20-30 minutes, until cooked through and the internal temperature reaches 165°F. Remove from the oven, let rest for 5 minutes, then slice.
In the meantime, drain the artichoke hearts and use a paper towel to absorb excess moisture. Place in a small bowl and mix with the olive oil and parmesan cheese. Season with salt and pepper.
To assemble the wraps, lay out the tortillas, top with mozzarella cheese, the sliced chicken, artichokes, and spinach. Fold the sides in, roll up, and slice in half.