Place each chicken breast between two sheets of plastic wrap and pound to an even ½-inch thickness. Season both sides with salt and pepper, then dredge in flour, shaking off the excess.
Heat olive oil and 1 tablespoon butter in a large skillet over medium-high heat. Sear the chicken 3–4 minutes per side until golden and cooked through (165°F internal). Transfer to a plate and tent with foil.
Lower heat to medium. Add the remaining butter, garlic, and shallot to the skillet; cook 1 minute until fragrant. Pour in the wine, scraping up the browned bits from the pan.
Add the chicken broth and artichoke hearts. Simmer uncovered for exactly 10 minutes, until the liquid reduces by about half and looks slightly syrupy.
Remove the skillet from the heat. Stir in the heavy cream and lemon zest, then whisk in the parmesan a little at a time until smooth. Return to low heat, nestle the chicken back into the sauce, and warm through for 2–3 minutes.
Off the heat, stir in the lemon juice, parsley, and red pepper flakes if using. Season to taste with salt and pepper. Serve immediately with extra sauce and artichokes spooned over each piece.