How to Make It
Bring a large saucepan of water to a boil over high. Core tomatoes; discard cores. Cut an “X” on bottom of tomatoes. Place tomatoes in boiling water, and cook until skins begin to loosen, 15 seconds to 1 minute (depending on ripeness). Plunge into an ice bath; let stand 1 minute, and drain. Peel skin off of tomatoes, and lay skins flat on a plate lined with a paper towel; pat dry. Slice tomatoes into 1/2-inch thick slices; set aside.
Place garlic on a cutting board; finely chop garlic, and sprinkle with 1/8 teaspoon of the salt. Using a chef’s knife, gather chopped garlic into a pile. Holding the blunt side of knife with both hands, press and scrape sharp edge of knife against pile of garlic, holding blade at a slight angle so it crushes garlic. Continue to press and scrape knife back and forth through pile until a paste forms, about 1 minute. Stir together garlic paste, mayonnaise, soy sauce, pepper, and 1/4 teaspoon of the salt. Set aside.
Heat 2 1/2 tablespoons of the oil in a small skillet over medium until shimmering. Add tomato skins, in batches, and cook until lightly browned and crisp, about 15 seconds. Transfer to a plate lined with paper towels, and sprinkle with 1/8 teaspoon of the salt.
Toss together arugula, lemon juice, and remaining 1 1/2 teaspoons oil in a medium bowl.
Spread 1 tablespoon of the mayonnaise mixture on each slice of bread; top with avocado slices, and sprinkle evenly with 1/4 teaspoon of the salt. Top each evenly with tomato slices and arugula; sprinkle with remaining 1/4 teaspoon salt. Top with crispy tomato skins. Serve immediately.