Pat chicken thighs dry with paper towels. Season with salt and black pepper.
In a large skillet or Dutch oven, heat 1 tablespoon of the olive oil over medium-high heat until shimmering. Add the chicken and sear until browned on the bottom, 5 to 6 minutes. Flip and sear until the second side is browned, 2 to 3 minutes more. Transfer to a plate.
Add the remaining 2 tablespoons olive oil, shallot, and zucchini to the skillet. Cook, stirring occasionally, until softened, about 3 minutes. Add orzo, garlic, and lemon zest. Stir to coat with the oil. Cook until lightly toasted and fragrant, 1 to 2 minutes.
Add stock, milk, and salt. Stir to combine, scraping up any browned bits from the bottom of the pan with a wooden spoon. Bring to a boil over medium-high heat, stirring frequently to keep the orzo from sticking. Reduce the heat to maintain a simmer.
Nestle the chicken into the orzo and pour in any accumulated juices. Cook uncovered, making sure the orzo is in the liquid at all times and stirring frequently, until orzo is tender, the chicken is cooked through and registers 75ºC/165ºF on a thermometer, and most of the liquid is absorbed, about 10 to 12 minutes.
Remove the pan from the heat. Add lemon juice and Parmesan cheese. Stir to combine. Let sit for 5 minutes before serving.
