Brush any dirt off the mushrooms with a clean dish towel or paper towel. Remove the stems from the mushrooms (reserve for making stock or chop and use in soup or stir-fry).

In a 1-gallon plastic zip-top bag or large bowl, mix together the flour, cornmeal, Old Bay Seasoning, paprika, garlic powder, onion powder, salt, cayenne, and black pepper.

Pour milk into a medium bowl and stir in the buffalo sauce. Transfer mushrooms to the bowl and toss until they're wet. Lift the mushrooms out with a slotted spoon and transfer them to the bag with the flour mixture. Gently shake the bag to coat the mushrooms. Set the bag aside and let the coating set while you make the tartar sauce.

To make the tartar sauce, mix all the ingredients together and chill in the refrigerator until you are ready to serve.

To fry the mushrooms, pour the oil into a dry, deep, pot to the depth of about 3 inches: mushrooms should be able to "bob" in the oil. Heat the oil to 350°F–this will take between 5 and 10 minutes over medium heat, depending on your stove. If you don't have a thermometer these are some other ways to judge whether your oil is hot enough; dip a wooden chopstick into the oil–if bubbles start to form, the oil is hot enough; pinch a small bit of the moistened flour batter and drop it in the oil–if it starts to bubble immediately, the oil should be ready.

Place a thick brown grocery bag on a cutting board or line a plate with paper towels. Working in batches, use a slotted spoon to lower 3 to 4 mushrooms into the oil. Turn mushrooms once or twice while frying. Fry until golden brown, 4 to 5 minutes per batch. Transfer to the brown bag or lined plate to drain.

To assemble the sandwiches, slather the bread on both sides with tartar sauce. Place a handful of lettuce, some tomato slices, and pickles on the bread then pile on the mushrooms. Serve with fries or chips.