Pat the chicken dry thoroughly using paper towels, then season generously on all sides with salt and pepper. In a 10-inch or larger skillet, heat the olive oil over medium-high heat until it shimmers. Working in batches if necessary, add the chicken and sear undisturbed until the bottom is deeply browned, about 6 to 7 minutes. Flip using tongs and sear the other side for another 6 to 7 minutes, until evenly browned. Transfer the chicken to a plate and set aside. Reduce the heat to medium and add the butter to the skillet. Once melted, add the chopped shallot, minced garlic, ½ teaspoon of salt, and ¼ teaspoon of pepper. Cook, stirring occasionally, until the shallots just begin to soften, about 1 minute. Sprinkle in the flour and stir to coat the shallots and garlic evenly, cooking for 1 more minute. Slowly pour in the half-and-half or milk and chicken broth, stirring constantly to eliminate any lumps and scraping up the browned bits from the bottom of the pan. Bring the mixture to a boil, then reduce the heat to maintain a simmer. Return the chicken and any accumulated juices to the skillet. Simmer for 3 to 4 minutes, or until the sauce has thickened enough to coat the back of a spoon and the chicken is fully cooked through. Stir in the lemon juice, then garnish with chopped parsley and lemon slices. Serve immediately.