Slice the leek into thin rounds and remove the sausage from its casings. Break the sausage into small pieces with your hands.
Heat the olive oil in a large deep skillet over medium-high heat. Add the sausage and cook for 7-8 minutes, letting it brown and develop crispy edges. Transfer it to a plate, leaving the drippings in the skillet.
Reduce the heat to medium-low. Add the butter and leek and cook for 10-12 minutes, stirring occasionally, until soft and lightly golden.
Add the garlic and thyme and cook for about 30 seconds, just until fragrant.
Stir in the orzo and cook for 1-2 minutes, stirring frequently to lightly toast the pasta.
Pour in the white wine and cook until it has reduced almost completely, scraping up any browned bits from the bottom of the skillet.
Add the chicken broth and bring to a gentle simmer. Cook for about 10 minutes, stirring occasionally, until the orzo is tender and creamy. Add a splash of warm broth if needed.
Return the sausage to the skillet and stir in the cream, Parmesan, and white pepper.
Cook on low heat for 1-2 minutes, stirring gently until the sauce becomes silky and well combined. Season with salt to taste.
Transfer to serving bowls and garnish with extra Parmesan, freshly ground black pepper, and lemon zest before serving.