In a large bowl, combine all the sausage making ingredients. Using a meat grinder, or in batches in a food processor, grind the mixture together. Form into 12 equal portions, flattening slightly into patties, to measure about 3 inches in diameter. Place a piece of cheese on top of 6 of the patties and top with the remaining patties, pinching the meat together to seal the cheese completely.

Preheat a grill. In a large skillet or saute pan, heat 1/4-inch of oil over medium-high heat. Add the stuffed sausage patties and cook until brown on both sides and the meat is cooked through, about 10 minutes. Remove from the heat and drain on paper towels.

Brush the sliced bread with some vegetable oil. Place the bread on the grill and cook until toasted with grill marks. Remove and set aside.

For the Poached Eggs: Pour cold water into a 10-inch saute pan to a depth of about 2 inches. Bring to a simmer, then reduce the heat so that the surface of the water barely shimmers. Add the vinegar. Break 4 of the eggs into individual saucers, then gently slide them out one at a time into the water and, with a large spoon, lift the white over the yolk. Repeat the lifting once or twice to completely enclose each yolk. Poach until the whites are set and the yolks feel soft when touched gently, 3 to 4 minutes. Remove the eggs with a slotted spoon and either serve immediately, or place in a shallow pan or large bowl of cold water. Repeat with the remaining eggs, adding more water as needed to keep the depth at 2 inches, and bringing the water to a simmer before adding the eggs.

To serve, place 1 grilled bread round on 6 plates. Top with 1 sausage patty and 1 poached egg. Drizzle 2 tablespoons of sauce over each egg and garnish with the chopped parsley. Serve immediately.

In a large saute pan, heat the oil over medium-high heat. Add the tasso and cook, stirring, for 1 minute. Add the shallots and garlic and cook, stirring, for 1 minute. Add the cream and bring to a boil. Lower the heat slightly and simmer until reduced by half, 3 to 4 minutes. Add the green onions, hot sauce, lemon juice, and salt. Add the butter and cook, stirring, until incorporated and thick. Remove from the heat and adjust the seasoning, to taste.