1. Grease 8 1/2 x 4 1/2-inch nonstick loaf pan. Melt butter in Dutch oven over medium-high heat. Add onion and cook until lightly browned, about 5 minutes. Stir in sage, fennel, and allspice and cook until fragrant, about 30 seconds. Add 4 1/4 cups water and sausage and mash with potato masher until water and sausage are fully combined. Bring to boil and stir in oats. Cover, reduce heat to low, and simmer gently, stirring occasionally, for 15 minutes.

2. Uncover and maintain gentle simmer, stirring frequently, until mixture is very thick and rubber spatula dragged across bottom of pot leaves trail for about 3 seconds, 15 to 18 minutes. Season with salt and pepper to taste.

3. Transfer mixture to prepared pan. Smooth top and tap firmly on counter. Let cool completely, then cover with plastic wrap and refrigerate until fully chilled and firm, at least 3 hours or up to 2 days.

4. Run thin knife around edges of goetta, then briefly set bottom of pan in hot water to loosen goetta from pan. Turn out goetta onto cutting board. Cut desired number of 1/2-inch-thick slices from loaf. Heat oil in 12-inch nonstick skillet over medium heat until shimmering. Add up to 4 slices of goetta and cook until well browned, about 5 minutes per side. Transfer to wire rack and let drain. Repeat as needed. Serve. (Wrap any remaining goetta in plastic wrap and refrigerate for up to 3 days, or slice, wrap, and freeze for up to 1 month. To cook from frozen, reduce heat to medium-low and increase cooking time to 7 to 9 minutes per side.)

Serves 6 to 8