Start by seeding the English cucumber, then cut it into even strips (julienne). If you are not using an English cucumber, sprinkle the strips with a little salt and place them on a paper towel for about 30 minutes to draw out excess moisture. Next, halve and seed the roma tomato. Salt the tomatoes lightly and place them cut side down on a cookie sheet to drain for about 30 minutes as well. This step prevents the wrap from becoming soggy.
Lay the tortilla wraps flat on a work surface. Evenly spread a layer of hummus over each wrap, leaving about a half-inch border clean on one of the long edges. This makes rolling easier and prevents the filling from spilling out.
Arrange the avocado slices evenly over the hummus layer. Then, add the prepared cucumber strips (from Step 1) and tomato slices (from Step 1) in a thin layer over the avocado. Top with the fresh baby spinach leaves. I like to add the spinach last to keep the leafy greens crisp and fresh.
Carefully roll up each wrap from the long edge, creating a long, skinny roll. Use a serrated knife to slice the roll into bite-sized pieces. This keeps the fillings neatly inside and makes for easier eating.
Arrange the sliced pieces on a plate with the cut sides up. Sprinkle the grated carrot over the top as a final touch, and serve immediately for maximum freshness.