Heat olive oil in a skillet over medium heat. Add onion and celery. Stir in 1/4 teaspoon salt and 1/4 teaspoon pepper. Sauté 5 minutes. Stir in garlic; sauté 2 minutes. Remove from heat; cool 5 minutes.
Combine onions, cheese, mustard, and 2 tablespoons lemon juice in a large bowl. Fold in crab. Fold reserved onion mixture into crab mixture. Set aside.
Combine egg yolks, 2 tablespoons lemon juice, remaining 1/4 teaspoon salt, and white pepper in a food processor; process until smooth. With processor running, pour oil through food chute in a slow, steady stream, and process until thick. Pulse in Worcestershire and hot sauce.
Stir in 1/2 cup aïoli mixture and 1/2 cup breadcrumbs. Form into 18 patties, about 1/4 cup each.
Combine remaining 1/2 cup breadcrumbs and seafood seasoning in a shallow dish. Dredge crab cakes in seasoned breadcrumbs.
Heat half of remaining oil in a large nonstick skillet over medium-high heat. Fry half of crab cakes in hot oil 2 to 3 minutes on each side until golden brown. Drain on paper towels. Repeat with remaining oil and cakes.
Place tomato slice on half of biscuit. Top with crab cake; dollop with aïoli and top with arugula leaves. Skewer with long wooden or bamboo pick to secure. Repeat.