Melt butter in a large Dutch oven over medium heat. Add onion, carrots, and celery with a pinch of salt. Cook, stirring occasionally, until the vegetables soften and the onion turns translucent, about 6-7 minutes. Add garlic and thyme; cook until fragrant, about 1 minute more.

Stir in the orzo and cook for 2 minutes, letting it toast slightly and absorb the butter. Pour in the chicken broth, scraping up any browned bits from the bottom of the pot. Bring to a boil, then reduce heat to maintain a gentle simmer. Cook until the orzo is just tender, about 10-12 minutes, stirring occasionally to prevent sticking.

Stir in the cooked turkey and simmer until heated through, about 3 minutes. Reduce heat to low and stir in the heavy cream, lemon juice, and Parmesan. Taste and adjust seasoning with salt and black pepper. The soup should be creamy and slightly thickened; if too thick, thin with a splash of broth.

Ladle into bowls and top with chopped parsley and extra Parmesan. Serve immediately with crusty bread.