Soak caul fat in tepid water for 10 minutes, to make it pliable.
Peel the thin outer membrane from the liver and cut into chunky rectangles about 1 by 2 inches, discarding veined sections. Sprinkle each chunk of liver with a light dusting of salt and pepper.
Drain the caul fat and carefully unfold. Cut pieces of caul fat large enough to wrap around each chunk of liver in a single layer. Surround the liver in orange slices, tucking a little piece of bay leaf inside each packet, then wrap with caul fat. Sprinkle more salt and pepper on the outside and thread the chunks on skewers, separating each chunk with half a bay leaf.
Preheat the grill or broiler to medium heat.
Grill the skewers for about 3 to 5 minutes per side, until the outside of each chunk is nicely browned and the inside is still pink.
Meanwhile, in a large saute pan, heat the extra-virgin olive oil. Saute the garlic until fragrant and add the dandelion greens. Toss the greens in the oil until wilted and soft. Season with salt and pepper. Remove from the heat and drizzle with some red wine vinegar.
Plate greens on a platter. Put the liver on the greens and squeeze the juice from the remaining orange slice on top. Serve with crusty bread.