First things first, cook your sushi rice according to the package instructions. A common ratio is one part rice to two parts water. Once cooked, let it cool slightly.
While the rice cools, prepare your seasoning mix. In a small bowl, combine the rice vinegar, brown sugar, and a pinch of salt. Stir until the sugar and salt are fully dissolved. Once the rice is slightly cooled, gently fold this seasoning mix into the rice.
Bring a small pot of water to a boil. Carefully lower the eggs into the boiling water and cook for 6-7 minutes for a perfect soft boil. Once done, immediately transfer them to an ice bath to stop the cooking. Peel them carefully when cool enough to handle.
Mince the garlic clove. For the vegetables, cut the cucumber and cherry tomatoes into small cubes. Thinly slice the spring onions. Use a vegetable peeler to create long, thin strips from the carrots.