Mix the crabmeat with the mayonnaise, mustard, paprika, cayenne, lemon juice, scallion and a pinch of salt in a bowl. Set aside.
Preheat the broiler. Brush both sides of the Texas toast with half of the melted butter. Place on a baking sheet and broil until golden brown on top, about 3 minutes. Remove from the oven and flip the bread; top with the crab mixture, spreading it almost to the edges. Sprinkle with the grated cheese.
Toss the asparagus with the remaining melted butter in a medium bowl and season with salt and black pepper. Arrange side by side on the toast, then arrange the cheese slices across the middle of the asparagus.
Return to the broiler until the asparagus is tender and the cheese melts, about 4 more minutes.