Wipe mushrooms with a paper towel or dish towel. Squeeze some of the excess moisture out. Cut into ¼-inch thick slices.
Prepare the wet batter: to a wide bowl, mix cornstarch, corn flour, and water. Add water and mix until it is no longer thick.
Prepare the dry batter: to a separate bowl, add cornstarch, corn flour, spices, and salt.
Coat the mushrooms: Coat each mushroom first in the wet batter and then the dry batter. Set aside on a plate.
Fry the mushrooms: Heat a cast iron or another pan over medium heat with avocado oil or another neutral oil. You will need enough oil to cover the base of the pan, which depends on the size of your pan. When the oil is hot, fry the mushrooms for about 3-4 minutes per side, or until golden-brown and crisp.
Make the aioli: In a small food processor, process all the ingredients. Adjust lemon juice and salt to taste.
Prepare the sandwich: Lightly drizzle olive oil on the bread and toast in a pan with the olive oiled side down. Spread aioli on both pieces. Add arugula, tomatoes, cucumbers, and fried mushrooms to one bread. Form the sandwich!