Cook the Sausage: Heat 1 teaspoon of the olive oil in a large, deep, lidded skillet or Dutch oven over medium-high heat. Add the sausage and cook for 5-6 minutes, stirring occasionally, until browned on all sides (for links) or broken into crumbles and well-browned (for bulk).
Transfer to a plate and set aside, leaving any drippings in the pan.
Cook the Onion: Reduce the heat to medium and add 2 teaspoons of olive oil to the same pan (no need to wash it first). Add the onion, sprinkle with ¼ teaspoon of the salt, and cook for 4-6 minutes until softened, stirring occasionally.
Add the garlic and cook for 1 minute until fragrant, scraping up any browned bits from the sausage.
Toast the Orzo: Add the dry orzo to the pan and stir to coat in the drippings. Toast for 1-2 minutes, stirring frequently, until the orzo smells nutty and turns very lightly golden.
Cook the Orzo: Pour in the chicken broth and stir to combine. Season with ¼ teaspoon of salt and the pepper. Bring to a boil, then reduce to a steady low simmer.
Cook, covered, for 10-12 minutes, stirring every couple of minutes to prevent sticking especially at the beginning, until the orzo is tender and has absorbed most of the liquid.
Finish: Remove from heat. Add the heavy cream and Parmesan, stirring until well incorporated.
Stir in the baby spinach in two additions, letting each batch wilt slightly before adding the next. Add lemon juice, and stir until smooth. Return the sausage to the pan and stir to combine. Let sit for 2-3 minutes to allow the sauce to continue to thicken and the sausage to warm back through.
Serve: Divide among bowls and top with extra Parmesan and more freshly ground black pepper.