Step 1
Heat 2 tablespoons of olive oil in a large skillet over medium-high heat. Pat the chicken thighs dry with paper towels and season them generously with salt. Place the chicken in the skillet and cook, turning occasionally, until browned on all sides—about 3 to 4 minutes per side. Avoid flipping the chicken prematurely to ensure it releases naturally from the pan. Once browned, transfer the chicken to a plate and set it aside.
Step 2
In the same skillet, add the remaining tablespoon of olive oil. Sauté the thinly sliced shallots and plum wedges, seasoning them with salt and a generous pinch of red pepper flakes. Stir occasionally until the shallots soften. Add the sherry vinegar and honey, bringing the mixture to a simmer. Return the chicken thighs to the skillet, including any accumulated juices, and cook for an additional 4 minutes, or until the sauce has thickened and the chicken is cooked through.
Step 3
Transfer the chicken thighs to a serving plate and pour the plum sauce over the top. Stir in the cold butter into the sauce, whisking until smooth and glossy. Taste the sauce and adjust the seasoning, if necessary, before serving.