Prepare a rolling station with your sliced veggies, a large shallow dish full of warm water, and your rice paper.
Place a sheet of rice paper in the water and let sit for 15 seconds. Remove from the water and layer the veggies towards the end of the rice sheet nearest to you. Layer a lettuce leaf with a few bell pepper strips, cucumber strips, and carrot stips. Top each with a thai basil leaf.
Carefully start rolling the rice paper tightly, similar to a burrito. Fold the sides in and roll as tightly as possible until completely rolled. Move to a plate and repeat with the last 7 spring rolls.
To make the peanut sauce, whisk all of the ingredients into a bowl except the water. Once mixed, add the warm water, 1 tbsp at a time until you reach the desired consistency.