Heat 1 tbsp. butter in a small saucepan over medium heat. Add shallots, garlic, and salt and pepper; cook for 1 minute. Add wine, bring to a boil, reduce heat to medium-low, and simmer until reduced by half, about 10 minutes. Remove from heat; strain through a sieve. Set divinity sauce aside.
Pour water into a medium saucepan to a depth of 2". Bring to a gentle simmer over medium-low heat. Whisk lemon juice, yolks, and 2 tbsp. water together in a heatproof bowl until frothy. Nestle bowl over simmering water and cook, whisking constantly, until pale yellow and thickened, 2–3 minutes. Remove bowl from heat and slowly drizzle in remaining butter in a thin stream, whisking constantly, to form a thick hollandaise sauce. Whisk in cayenne and salt. Cover to keep sauce warm.
Fill a large tall pot with at least 6" of poaching liquid (for every 4 cups of water, add 1⁄2 cup vinegar and 1⁄2 tsp. salt). Bring to a boil; reduce heat to medium-high to maintain a very gentle boil. Quickly crack each egg into the pot while holding your hands about 3" above the water. Poach eggs (see Perfect Poaching), without stirring, until yolks are set but still runny in the middle, 4 1⁄2–5 minutes. Using a slotted spoon, transfer eggs to a paper towel–lined plate; trim off trailing egg whites, if you like. Set oven rack 4" from the broiler; preheat. Put muffin halves on a baking sheet, cut side up. Arrange 3 slices of tasso on each, drizzle tasso with divinity sauce, and top each with a tomato slice. Broil until tomatoes are bubbly, 3–4 minutes. Divide muffin halves between plates, top each with a poached egg, and spoon hollandaise over the top.