Pulse shrimp in food processor until finely ground. Scrape down sides and add cream. Pulse a few more times to a fine puree.

Combine crab, shrimp mousse, herbs, lemon balsamic, and 1 egg in a large bowl and fold gently with a spatula until combined, being careful not to break up the large lumps of crab. Divide mixture into 8 balls and firmly press into 1/2-inch-thick disks. Place cakes on rimmed baking sheet lined with parchment paper, cover tightly with plastic wrap, and refrigerate for 30 minutes.

Place remaining egg in a small bowl and beat thoroughly. Mix bread crumbs and seasoning in a second small bowl. Working one crab cake at a time, dip in egg, then in bread crumbs, pressing down gently to adhere. Return to baking sheet, and repeat with remaining disks.

Meanwhile, poach eggs: Bring water, salt and vinegar to a boil in a large, high side sauté pan. Reduce heat to maintain a low simmer. Crack 1 egg into a glass measuring cup, hold spout close to water's surface, and let egg slip gently into water. Repeat with rest of eggs. Cook until eggs are softly set, 2 to 3 minutes, flip eggs and cook 30 more seconds. Using a slotted spoon, transfer as done to a large bowl of ice and cold water.

Heat 1 tablespoon oil in a skillet over medium heat until shimmering. Place 4 cakes in skillet and cook without moving them until golden brown, 3 to 4 minutes. Using 2 spatulas, carefully flip cakes, add 1 tablespoon oil, reduce heat to medium-low, and continue to cook until second side is golden brown, 4 to 6 minutes. Transfer to a plate and put in a 200° oven to keep warm. Wipe out skillet and repeat with remaining 4 cakes and remaining 2 tablespoons oil.

Set a bowl of lukewarm water to the side of stove. Add yolks to a slightly smaller bowl, then set bowl of yolks over (but not touching) a saucepan of barely simmering water (lift bowl periodically to check that water is not boiling). Whisk in balsamic, mustard, salt, and sriracha chili. Whisking constantly, drizzle in melted butter--a few drops at first, then in a thin, slow stream, until incorporated. Add in tablespoon of chipotle oil. Keep whisking until thick enough for the whisk to leave faint trails. Set bowl in bowl of lukewarm water and cover; whisk occasionally until ready to serve. If sauce breaks (you'll see oily butter separating out), slowly whisk in 1 tbsp. cold water or cold whipping cream.

Reheat poached eggs: Immerse eggs in water that's just hot to touch (but not hot enough to cook them further) until they feel warm, about 5 minutes. Lift each out with a slotted spoon and rest, still in spoon, on paper towels for a moment to drain briefly.

Put crab cakes on plates and slip a poached egg on each. Spoon about a little hollandaise sauce on top of each, and sprinkle with chives.