Make the sausage. Toast the cumin and fennel seeds in a skillet over medium heat, stirring constantly for 3 to 5 minutes, or until they emit their fragrance. Combine the cumin, fennel, and caraway seeds, chiles, paprika, 1 tablespoon of salt, and the pepper in a spice grinder; pulse to a fine grind, 45 to 60 seconds.
Pound the garlic and ½ teaspoon of salt to a paste in a mortar (or mince the garlic with the salt until it turns to a paste). Combine the garlic paste with the ground spices, and oil in a small bowl and mix well. Toss the seasonings with the lamb and pork in a medium stainless bowl, cover, and refrigerate overnight.
Grind the meat through the medium plate of a meat grinder or stand mixer grinding attachment and into a large bowl or pan, passing the mixture through twice. Mix the ground meat well with your hands.
Portion the sausage into 1/4-cup mounds (to make about 32) on two parchment-lined baking sheets. Shape portions into 4-1/2- by 1-inch links. Alternatively, shape them into ½-inch thick patties about 3 inches long in diameter,Press a 1-inch wide well in the center of each patty, flattening the meat in the well about 1/3 inch thick, to help the centers dook more evenly as the meat shrinks. Refrigerate, covered, until ready to grill.
Make the white beans. Heat the oil in a large sauté pan over medium-high heat. Add the diced Serrano ham and sauté until crispy and dark brown, 6 to 8 minutes; remove from the pan and set aside. Add the garlic, onions, and bay leaf to the pan and turn the heat to medium. Cook the vegetables, stirring, until they begin to caramelize, about 12 minutes. Remove the bay leaf and stir in the cannelloni beans, thyme leaves, parsley, salt and pepper. Cover and refrigerate 4 to 6 hours to allow the flavors to blend. Bring the beans to room temperature before serving.
Grill the sausages over medium-high heat on a preheated gas or charcoal grill until medium or medium well done, 12 to 15 minutes for the links and 6 to 8 minutes for the patties. Don’t prod the meat too much as it cooks. Grill in two batches if necessary, but for optimal flavor and texture, serve one batch immediately after cooking. Spoon ½ cup of the beans onto each plate and sprinkle with 1 tablespoon of the Serrano ham. Top with 4 of the grilled sausage links or patties and garnish with 2 thyme sprigs.