Soak the vermicelli noodles in warm water until softened, then drain and add to a large mixing bowl. Add the carrots, spring onions, garlic, ginger, mint, bean sprouts, soy sauce and sesame oil to the bowl and toss everything together.
To assemble the spring rolls, mix a little flour and water together to make a smooth paste. Lay one spring roll wrapper out on a clean surface and cover the rest with a damp tea towel.
Add about 1 tablespoonful of mixture to the centre of the wrapper, just below the middle. Fold the bottom edge over the filling, then fold the sides over the top, so you have a rough rectangle forming a sort of envelope. Roll up the wrapper tightly into a neat sausage shape around the filling and seal the edge with a little flour-water paste.
Brush with oil and place on a lined baking tray, then repeat with the remaining mixture and wrappers.
Heat the air fryer to 200°C/400°F.
Place about 4 spring rolls in the air-fryer basket at any one time, making sure there is plenty of space between them, and cook for 15–17 minutes, until crisp and golden.