Mix one 5.2-oz. package Boursin Garlic and Fine Herbs cheese, 1 tsp. finely grated lemon zest, 2 Tbsp. fresh lemon juice, 1 Tbsp. finely chopped parsley, and ¼ tsp. cayenne pepper in a small saucepan to combine. Gently fold in 8 oz. jumbo lump crabmeat, picked over, until just combined, taking care not to break it up too much. Place pan over medium heat and cook, stirring occasionally, until mixture is just warmed through, about 3 minutes. Reduce heat to lowest setting and keep filling warm.

Whisk 12 large eggs in a large bowl until smooth. Set aside.

Place 32 Ritz crackers (about 1 sleeve) in a large resealable bag, close, and crush to coarse crumbs with a rolling pin or heavy pot.

Melt 2 Tbsp. unsalted butter in a small nonstick skillet over medium heat. Cook crackers, stirring often, until golden brown, about 5 minutes. Transfer to a bowl; let cool.

Wipe out skillet and melt 1 Tbsp. unsalted butter, swirling pan, over medium-low heat. Pour in one quarter of reserved eggs; season with kosher salt. Cook, stirring in small circles around pan with a heatproof rubber spatula, until small curds form, about 2 minutes. Continue to cook without stirring until eggs are nearly cooked through, about 1 minute longer. Tap pan firmly against stove to even out eggs, then remove from heat and tuck any wispy edges under. Spread one quarter of filling over 1 side of omelet, then fold other side up and over filling. Slide omelet onto a plate and rub a little more butter on top (to put some gloss on it). Repeat process with remaining eggs and 3 Tbsp. unsalted butter, using 1 Tbsp. per omelet, to make 3 more omelets.

Shower omelets with cracker crumbs; serve with Tabasco. Do ahead: Filling can be made 1 day ahead. Let cool; cover and chill. Reheat over low, stirring gently.