Bring broth and 2 cups water to simmer in a medium saucepan. Turn heat to low to keep warm.
Warm olive oil in a heavy pot over medium heat. Add onion and cook, stirring, until softened, about 3 minutes. Add sausage and cook, stirring often and breaking up into small pieces, until it loses its pink color, about 5 minutes. Add rice and cook, stirring, for 1 minute. Add wine and cook until alcohol evaporates, about 2 minutes.
Add about 2 cups warm broth mixture and simmer, stirring frequently, until rice absorbs liquid. Continue to add liquid, about 2 cups at a time, stirring occasionally, until rice is creamy and soft, about 20 minutes (you may not use all of the liquid). Add spinach and stir until wilted, about 2 minutes.
Remove pot from heat, stir in cheese and butter and season with salt. Serve immediately.