If grilling or broiling, heat should be medium-high and rack about 4 inches from fire. Put fennel and garlic into a food processor and pulse until just chopped; remove to a large bowl. Put pork fat in processor and grind until just chopped; add to bowl. Working in batches, process meat with fennel seeds, caraway, if using and 1 teaspoon salt and 1/2 teaspoon pepper, until meat is just chopped (be careful not to over-process). Add to bowl and mix well. Shape mixture into 8 patties.
To broil or grill, cook about 5 minutes on each side, turning once after 4 or 5 minutes and again as necessary, 8 to 10 minutes total. For stovetop, heat a large skillet over medium heat for 2 or 3 minutes, then add patties; cook undisturbed for about 3 minutes, then rotate them so they brown evenly. When browned, turn. Total cooking time is about 10 minutes. (They can remain ever-so-slightly pink in the center.)
Garnish with peeled orange slices, chopped olives, chopped parsley, chopped roasted red pepper and fennel slices, to taste.