1. Preheat the vegetable oil in a deep fryer or a large, deep saucepan to 180°C (350°F).
2. In a food processor or blender, combine the sun-blushed tomatoes, mayonnaise, chopped garlic, lemon juice, salt, and pepper. Blend until smooth. Adjust the seasoning to taste, and transfer the aioli to a serving bowl. Set aside.
3. In a large mixing bowl, whisk together the flour, cornflour, baking powder, and salt for the tempura batter. Slowly pour in the sparkling water while whisking continuously until the batter is smooth and lump-free.
4. Cut the leftover fridge vegetables into bite-sized pieces suitable for tempura. Dip each vegetable piece into the tempura batter, ensuring they are well-coated.
5. Carefully place the battered vegetables into the preheated oil, a few pieces at a time, making sure not to overcrowd the pan. Fry for about 2-3 minutes or until the tempura turns golden and crispy. Use a slotted spoon or tongs to remove the vegetables and transfer them to a plate lined with paper towels to drain excess oil. Repeat the process until all the vegetables are fried.
6. Once all the tempura vegetables are ready, serve them warm alongside the sun-blushed tomato aioli. You can garnish the dish with a sprinkle of fresh herbs, such as basil or parsley, if desired.