Make crabcakes: Melt butter in a large frying pan over low heat. Add garlic, celery, and onion and cook, stirring often, until translucent but not browned, 8 to 10 minutes. Add chile flakes and flour and cook, stirring, until flour smells toasted, about 30 seconds. Stir in cream and parsley. Remove from heat and let mixture cool.
Meanwhile, gently squeeze water from crab over a colander. In a medium bowl, whisk together mayonnaise, egg yolk, mustard, salt, and black pepper. Stir in 1/3 cup panko, the crab, and cream mixture.
Put about 2 cups panko on a large plate. Form crab mixture into scant 1/2- or 1/3-cup patties (for 6 or 8 crabcakes, respectively). One at a time, set patties in panko, press lightly to help bread crumbs adhere, and turn with a thin metal spatula; press lightly on second side. Transfer to a large plate, cover, and chill at least 1 hour and up to 1 day.
Meanwhile, poach eggs: Bring a large, deep frying pan of lightly salted water to a boil. 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. Using a slotted spoon, transfer as done to a large bowl of ice and cold water.
Heat oil in a large frying pan over medium heat. Cook crabcakes, turning only once, until dark golden brown on both sides, 8 to 10 minutes total. (If making 8 crabcakes, you may need to cook in batches; if so, wipe out pan and add a fresh 3 tbsp. oil for second batch.) Transfer to a plate and put in a 200° oven to keep warm.
Make hollandaise sauce: 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 lemon juice, mustard, hot sauce, salt, and white pepper. Whisking constantly, drizzle in melted butter--a few drops at first, then in a thin, slow stream, until incorporated. 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 crabcakes on plates and slip a poached egg on each. Spoon about 1 1/2 tbsp. hollandaise sauce on top of each, and sprinkle with chives.
*Find panko with regular bread crumbs at your grocery store.
Make ahead: Crabcakes, through step 2, up to 1 day, chilled. Poached eggs, up to 1 day, covered and chilled in water. Hollandaise sauce, up to 1 hour at room temperature, covered. To reheat sauce, set the bowl over a saucepan of warm (120°) water and gently rewarm for 5 minutes, whisking every now and then.