- If making pasta to serve with chicken piccata: Boil pasta until al dente, according to package directions, then drain and toss with a little olive oil to prevent sticking.  Set aside. 
- Add chicken breast to a cutting board.  Hold your knife parallel to the board and carefully slice the chicken from right to left (if you’re a righty)… opening the chicken breast up like a book.  Slice all the way through, so you now have 2 thinly sliced pieces of chicken. Repeat with other chicken breast. 
- Season chicken with salt, pepper, and thyme.  Add flour to a shallow bowl, and add basil and paprika, stirring to combine. 
- Dredge chicken pieces in flour, then set on a plate. 
- Add butter and oil to a large skillet and heat over MED-HIGH heat.  Once hot, add chicken, 2 pieces at at time, and cook for about 4 minutes per side, or until chicken is golden brown and cooked through.  Remove chicken to a plate and repeat with remaining chicken pieces.  Watch the chicken as it cooks, and if it looks like it's getting too brown too quickly, reduce your heat a little. 
- Reduce skillet heat to MED.  Add shallots and garlic and cook 1 minute, stirring often. 
- Stir in wine, scraping the bottom to loosen any browned bits. Cook for 2 minutes over MED heat. 
- Stir in chicken broth, lemon juice and capers. Bring sauce to a low boil and then simmer for 3-5 minutes.   
- In a small mixing bowl, whisk together heavy cream and cornstarch until smooth. Stir mixture into sauce and cook 2-3 minutes, or until thickened to a sauce that will easily coat the back of a spoon. 
- Return chicken pieces to skillet and coat with sauce.  Add a few lemon wedges if you'd like. 
- Serve chicken sliced, over a bed of pasta that’s been tossed with plenty of sauce and sprinkled with lemon zest, parsley, and basil.  Or you can serve the chicken as is, with some vegetables alongside.