Preheat oven to 375 degrees F.
Stir oil, tamari and paprika together in a medium bowl. Add shiitakes and stir until all the liquid is absorbed. Spread on a rimmed baking sheet and roast, turning once, until golden brown on both sides, about 30 minutes.
Toast bread. Stir mayonnaise and garlic together in a small bowl.
Spread 1 tablespoon of the mayonnaise mixture on each of 4 pieces of toast. Divide avocado, tomato, lettuce and the roasted shiitakes over the toasts. Top with the remaining toasts.
