Season the chicken breasts with salt and pepper. Heat olive oil in a large deep skillet or Dutch oven over medium-high heat. Sear the chicken skin-side down for about 5-6 minutes until golden and crispy. Flip and cook for another 3-4 minutes before removing them from the pan and setting them aside.
Lower the heat to medium and add the butter and sliced leeks. Cook for 5-7 minutes, stirring occasionally, until softened and they reduce in size by about half. Season with a generous pinch of salt. Stir in the minced garlic and cook for another minute until fragrant.
Pour in the white wine, scraping up any browned bits from the pan, and let it simmer for 2-3 minutes until reduced by half. Stir in the orzo and toast it for 1-2 minutes for a nuttier flavor.
Add the chicken stock, Dijon mustard, and lemon juice along with another pinch of salt. Stir well and bring to a simmer. Add half of the cream and stir until combined. Return the chicken breasts to the pan, skin-side up. Nestle in the fresh thyme sprigs and reserved dark green leek tops on top. Cover and let everything simmer on low heat for 15-20 minutes, stirring occasionally, or until the orzo is tender and the chicken is cooked through (internal temp 165°F).
When the chicken is cooked through, remove it from the pan. Stir the rest heavy cream into the orzo along with Parmesan cheese, a little more lemon juice and black pepper. Adjusting seasoning if needed. If the sauce is too thick, add a bit more stock or cream.
Slice the chicken breast and serve it on top of a plate of orzo. Garnish with black pepper and parmesan.