Make the sauce: add mayonnaise, peppers, capers, pickles, lemon juice, chives, tarragon, mustard, and Old Bay seasoning to a bowl; whisk to mix.
Season to taste with black pepper; sauce can be refrigerated, covered, for at least 1 week; bring to room temperature before serving.
The crabs: melt the butter in a small saucepan over med-high heat.
Add in garlic, shallot, and Old Bay seasoning; cook until the garlic and shallot have lost their rawness, about 2 minutes; they should be soft and translucent; do not let them brown; set flavored butter aside.
Set up grill for direct grilling; preheat to high.
When ready to cook brush and oil the grill grate; brush the crabs on both sides with some of the flavored butter.
Place the crabs on the hot grate and grill until cooked through, about 2-4 minutes per side, basting with some of the flavored butter.
When done, the shells will turn bright red.
Brush the bread slices with the remaining flavored butter and grill them as well, about 1 minute per side.
To serve: slather the toast with some of the Old Bay Tartar Sauce; place a lettuce leaf, a few tomato slices, and 2 soft-shell crabs on top.
Serve with the remaining tartar sauce on the side.