Pat the chicken thighs dry. Season both sides with the salt and pepper, then dredge in the flour and shake off the excess.
Heat the olive oil in a 12-inch cast iron or heavy skillet over medium-high until shimmering. Add the thighs smooth side down without crowding (work in two batches if needed). Cook without moving until golden and they release easily, 3 to 4 minutes. Flip and cook the other side until golden, 3 to 4 minutes more. Transfer to a plate.
Reduce the heat to medium. Pour off all but about a tablespoon of fat. Add the smashed garlic and rosemary and cook, stirring, until fragrant and just starting to turn golden, about 1 minute. (If using jarred garlic, cook only 30 seconds.)
Add the wine and scrape up the browned bits from the bottom of the pan. Simmer until reduced by about half, 2 to 3 minutes. Add the chicken stock.
Return the chicken and any juices to the pan and spoon the sauce over it. Simmer gently, uncovered, spooning sauce over the chicken every few minutes, until the thighs reach at least 165°F (175°F is ideal for thighs) and the sauce has thickened slightly, 6 to 10 minutes. If the sauce gets too thick before the chicken is done, stir in a splash of stock.
While the chicken simmers, mash the softened butter and the sauce flour together with a fork into a smooth paste.
Transfer the chicken to a plate and remove the rosemary sprig. Stir the lemon juice into the sauce, then whisk in the butter paste a little at a time. Simmer gently, whisking, until the sauce thickens and turns glossy, about 1 minute. Taste and add salt if needed.
Return the chicken to the skillet, spoon the sauce and garlic over it, and sprinkle with parsley.
Notes
No wine: replace the wine with more chicken stock plus 1 teaspoon white wine vinegar.Sauce too thin: after removing the chicken, simmer the sauce a minute or two longer after whisking in the butter paste, or mash a little more flour into the paste. Too thick: stir in a splash of stock.Chicken breasts: slice horizontally into thin cutlets and cook to 165°F.Storage: refrigerate in an airtight container for 3 to 4 days.Reheating: warm in a covered skillet over medium-low with a splash of stock, or microwave at 50% power until heated through.