Lay your sliced bread onto a baking sheet and brush or drizzle both sides with butter. Season with salt and pepper. Place under the broiler until tops are lightly browned. Remove and immediately rub your peeled garlic clove onto each slice. Set aside.
Dry your filets with a paper towel and season WELL with salt and pepper. Place a heavy saute pan over high heat until it gets very hot. Add, 2-3 tbsp of butter to the pan and immediately add your filets swirling the butter around each filet using the pan handle to do so. Don't move your filets! Wait about 4-5 minutes and flip when one side starts to brown. Allow the other side to sear until nicely browned. Internal temperature should reach about 140 degrees for medium steak. Take off heat and set aside. Slice filet very thinly right before your ready to assemble.
To make your Bearnaise sauce, add 2 tbsp of butter to a sauce pan over medium heat. Add your shallots, vinegar and tarragon. Simmer for about 5 minutes to allow the shallots to soften and vinegar to cook off. Don't let the shallots burn! Turn off heat and allow to cool.
Cook your asparagus according to directions (if using a steam bag). Otherwise, bring salted water to a boil in another sauce pan and toss in your asparagus for a few minutes (until just cooked through) not too soft! Rinse with ice cold water and then cut into desired length. Set aside.
Add your egg yolks to the shallots and whisk. Turn heat back on to the lowest setting and while whisking, stream in your butter slowly until fully incorporated. Whisk your butt off making sure to scrape the bottom of the pan. The sauce will slowly start to thicken as the eggs cook. Once the sauce is thick enough, (think creamy soup) turn off the heat. Finally, whisk in your lemon juice and add salt and pepper to taste. Set sauce aside. *Your sauce will thicken as it sits. If needed, add a little water to loosen up.
When ready, start to assemble your crostini directly on your baking sheet. Place one to two slices of filet onto each followed by two asparagus spears, then a spoonful of the crab meat. Cover with tin foil and place in a 350 F oven until all components are warmed through (about 10 minutes). The bottom of the crostini will also get a chance to crisp up! Take out and place on serving platter with sauce drizzled generously over each.