In a shallow bowl, stir together 1 tablespoon olive oil along with the oregano, paprika, onion powder, garlic powder, salt and pepper. Add chicken to the bowl and coat in the seasoning mixture.
In a medium skillet over medium heat, heat the remaining tablespoon olive oil. Transfer the chicken to the skillet and cook until the juices run clear, about 3-4 minutes per side. Remove from heat and allow it to cool, then slice each breast into strips.
In a steamer set over boiling water, steam broccoli, covered, until crisp-tender, 2-3 minutes.
In the center of each tortilla wrap, spread the sour cream evenly, then add the chicken, broccoli and cheese. Bring the bottom edge of the wrap tightly over the filling, folding in the sides, then roll until you reach the top of the wrap.
Add the wraps to a panini or the skillet used to cook the chicken with the seam side down, and press gently for about 3-4 minutes total, until golden brown and the cheese has melted. Serve immediately.