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.