In a large, oven-proof pan with a lid, heat the oil. Season the rabbit and 1/2 cup of the flour with salt and pepper. Dredge the rabbit pieces in the seasoned flour, coating each side completely. Lay the rabbit, skin side down in the oil and brown for 3 to 4 minutes on each side. Remove the rabbit from the pan and set aside. Add the sausage and brown for 2 to 3 minutes. Add the onions. Season with salt and pepper. Saute for 2 to 3 minutes or until tender. Add the mushrooms and garlic. Saute for 2 minutes. Season with salt and pepper. Add thyme and bay leaves. Add the rabbit to the vegetable mixture. Add the beer and chicken stock. Bring the liquid up to a simmer and cover. Cook the rabbit until very tender, about 30 to 35 minutes, skimming off the fat. Remove the rabbit pieces from the pan and set aside.
Blend the remaining flour and butter together into a smooth paste. Whisk the paste into the hot liquid. Bring the liquid to a simmer and cook for 3 to 4 minutes. Add the rabbit back to the pan and continue to cook for 5 minutes. Stir in the parsley. Season with salt and pepper, if needed. Serve the rabbit with the leek rosti and garnish with parsley.
Place the potatoes in a saucepan, cover with water and season with salt. Over medium heat, bring the water to a boil, reduce the heat to medium low and cook until the potatoes are tender. Remove from the water and cool completely. Peel the potatoes and pass through a coarse grater. In a large nonstick saute pan, over medium heat, melt the butter. Add the leeks. Season with salt and white pepper. Saute for 2 minutes. Add the potatoes and mix thoroughly. Using the back on a wooden spoon press the potato mixture firmly into the pan. Reduce the heat to low and cook until the potatoes are crispy and golden brown. Using a spatula, flip the potato cake over and continue cooking the other side, adding more butter, if needed. Remove from the pan and slice into individual servings.