Warm the olive oil in a large skillet set over medium heat until the surface begins to shimmer.

Generously sprinkle both sides of the chicken breasts with salt and pepper. Arrange the seasoned chicken in the skillet and sear for about 5 minutes, or until the underside is well browned.

Move the browned chicken, seared-side facing upward, into the bottom of a 6-quart (or larger) slow cooker, keeping the pieces in a single layer.

Pour in the chicken broth, add the fresh lemon juice, and scatter the smashed garlic cloves over the top. Cover with the lid and set the slow cooker to LOW. Let the chicken cook until thoroughly tender and an internal temperature of 165°F is reached—this will take between 3 and 4 hours.

While the chicken cooks, combine the softened butter and flour in a small bowl. Use your fingertips to work the flour into the butter until a smooth paste forms. Set aside.

Once the chicken is fully cooked, transfer the pieces to individual serving plates or a platter.

Carefully pour the cooking liquid and garlic from the slow cooker into a small saucepan. Bring the mixture to a boil over medium-high heat.

Add the prepared butter-flour mixture to the sauce, whisking continuously until it is fully dissolved and the sauce begins to thicken. Continue stirring as it cooks for an additional 3 to 4 minutes.

Drizzle the thickened garlic-lemon sauce over the chicken. Optionally, finish with a sprinkle of chopped parsley just before serving.