In a 12 to 14-inch saute pan, heat 4 tablespoons olive oil until smoking. Add onions and cook until golden brown, about 8 to 10 minutes. Add Cinzano and cook until liquor is evaporated. Place onions in separate bowl and set aside. Season venison with salt and pepper and dredge in seasoned flour.
In a clean 12 to 14-inch saute pan, heat oil until smoking. Place venison pieces and cook until dark golden brown on one side. Turn and cook 1 minute on other side and remove to warm plate. Add potatoes and cook until light brown, about 4 to 6 minutes. Add speck, remaining Cinzano, chicken stock, tomato sauce and onions and reduce by half. Add venison and cook 1 minute. Remove meat to platter and spoon sauce around.
Saute the onion and garlic in the olive oil over medium heat until translucent, but not brown (about 10 minutes). Add the thyme and carrot and cook 5 minutes more. Add the tomatoes. Bring to a boil, lower the heat to just bubbling, stirring occasionally for 30 minutes. Season with salt to taste. Serve immediately, or set aside for further use. The sauce may be refrigerated for up to one week or frozen for up to 6 months.