Cut each shrimp crosswise into 5 pieces. Blot with paper towels to dry. Julienne carrots into thin matchsticks about 2 1⁄2 inches long. Slice onion into similar-size matchsticks.

Whisk egg and ice-cold water in a medium bowl. Set aside 2 tablespoons cake flour in a small bowl. Sift the remaining 1 cup cake flour and potato starch into another bowl. Add the sifted flour mixture to the egg mixture. Using a whisk, lightly combine the egg and flour mixtures.

Combine the sliced shrimp, vegetables and herbs in a medium bowl. Add the reserved 2 tablespoons flour; toss to coat the shrimp and vegetable pieces evenly.

Line a sheet pan or large plate with paper towels. Combine grapeseed oil and sesame oil in a Dutch oven. Heat the oil to 335°F.

Place about ¼ cup of the flour-coated shrimp and vegetable mixture in a small bowl. Add about 2 tablespoons of the chilled tempura batter to lightly coat the mixture. Slide it into the hot oil.

When the fritters turn slightly crisp and the bubbles nearly subside, flip them over. Fry until lightly golden on both sides. Remove and transfer to the prepared paper-towel-lined pan.

Serve the tempura immediately with sea salt, lemon wedges and/or soy sauce.