Season flour with salt and pepper. Dredge chicken tenders in flour mixture until coated.
Heat 1 tablespoon olive oil and butter in a large pan over medium-high heat. Add chicken and brown for 2 to 3 minutes per side. Remove from the pan and keep warm.
Reduce heat to medium and add remaining 1 tablespoon olive oil. Add garlic and saute until fragrant, about 30 seconds, being careful not to burn it.
Pour wine into the pan and bring to a boil while scraping the browned bits of food off the bottom of the pan with a wooden spoon. Add chicken stock and cook until sauce has reduced, about 10 minutes. Add half-and-half, Parmesan cheese, and lemon juice; let reduce for 10 more minutes.
Dissolve cornstarch in water and add to the pan. Add chicken and allow to heat through, about 10 more minutes. Season with salt and pepper and serve.