Directions

• Preheat grill to high (450°F to 500°F). While grill preheats, process tofu, 1/3 cup oil, 2 teaspoons lemon juice, 3/4 teaspoon kosher salt, smoked paprika, and grated garlic in a food processor until creamy and smooth, about 30 seconds, stopping to scrape down sides of processor bowl after 15 seconds. Transfer aioli to a small bowl, cover, and set aside.
• Stir together shallot, serrano chile, 1/4 teaspoon kosher salt, and remaining 1 tablespoon lemon juice in a small bowl. Let stand 5 minutes. Stir in cherry tomatoes and 1 1/2 tablespoons oil; set aside.
• Drizzle 1 tablespoon oil evenly over corn and shishito peppers; toss to coat. Arrange corn and peppers on oiled grates; grill vegetables, uncovered, turning occasionally, until tender and charred in spots, 3 to 5 minutes for shishito peppers and 15 to 18 minutes for corn. Transfer vegetables to a cutting board.
• Brush both sides of bread slices evenly with remaining 2 tablespoons oil. Arrange bread on oiled grates; grill, uncovered, until lightly charred and crisp, 1 to 3 minutes per side. Remove toasted bread slices from grill, and rub on both sides with whole garlic clove.
• Cut corn kernels from cobs; discard cobs. Chop shishito peppers into bite-size pieces. Add corn, shishitos, 1 to 2 tablespoons aioli, and remaining 1/2 teaspoon kosher salt to tomato mixture; toss until evenly combined.
• Spread 2 tablespoons aioli on one side of each toasted bread slice. Top evenly with corn mixture (a heaping 1/2 cup per slice) and any remaining juices in bowl. Garnish with flaky salt. Serve with additional aioli, if desired.