Heat olive oil in a large skillet over medium-high heat.
Add in sausage, breaking it up as it cooks, until browned, 4-5 minutes.
Add in the red onion, fennel, garlic, thyme, salt, and pepper; cook, stirring frequently, for about 4 minutes or until the vegetables wilt and the onions become translucent.
While the vegetables are cooking, start the polenta: In a saucepan, combine 2 ½ cups chicken broth and milk; season with salt and pepper.
Place over med-high heat and bring to a simmer.
Back to the vegetables: once the vegetables have wilted, add in the white wine and remaining 1 ½ cups chicken broth to the skillet; increase heat to high and bring up to a simmer.
Cook about 4-5 minutes, to reduce liquids by half; stir in the chopped parsley.
To the simmering chicken stock/milk, add in the polenta; whisk constantly until the cornmeal masses together.
Add in the butter and grated cheese; stir to combine (if polenta becomes too thick, add more broth or milk).
Serve polenta topped with ragout; garnish with more Parmigiano-Reggiano.