Place two dinner plates and a warming tray in a 200 degree heated oven. Prepare boiled water with 2 tablespoons of olive oil for the pasta. (Add pasta to water when chicken is being browned)
Butterfly cut the chicken breasts in half and lightly pound with a tenderizing kitchen tool on both sides until thinned out.
Add 2-3 tablespoons of olive oil to a large frying pan over medium heat. (I prefer avocado oil as it has a higher smoke/flash point) Either works well. (Do NOT use vegetable cooking oil. It will not taste the same).
While the oil is heating, combine flour, sea salt, and ground pepper into an average bowl or deep plate.
Use the flour mixture to dust the chicken fillets on both sides completely. Do not shake off excess as this will be needed in the sauce later.
Place the chicken fillets in a frying pan that is large enough that doesn't crowd the pieces. Cook for about 7 minutes or until lightly browned, turning the fillets several times. DO NOT overcook.
Remove chicken fillets from the pan allowing them to drip free of excess oil before placing them on your pre-heated warming tray from the oven.
To make the piccata sauce, add the remaining 2 tablespoons of olive oil to the same frying pan along with the chicken drippings at medium temperature. Mix in sliced garlic and saute' until translucent. (About 1 minute) Reduce heat to simmer.
Add white wine to sauteed garlic pan mixture and stir reducing down to half volume.
Combine chicken stock, lemon juice, capers, mushrooms and thin lemon slices into the pan stirring with a wooden scraper until thickened. (Leftover flour, salt, and pepper mixture can be used to thicken if needed to desired taste).
Turn off heat and mix in butter and parsley. Serve piccata sauce over chicken fillets and linguine pasta.