Combine the mayonnaise, garlic, lemon juice, salt and pepper in a small bowl. Stir until smooth and set aside.
Heat the olive oil and butter in a large frying pan over medium high heat.
Add the gnocchi and cook for 8 to 10 minutes, stirring occasionally, until golden and crispy on all sides.
Add the garlic and cook for 1 minute until fragrant.
Remove the pan from the heat and toss through the lemon zest, parmesan, salt and cracked black pepper until evenly coated.
Scatter over the fresh basil and serve immediately with the garlic aioli. Garnish with lemon wedges.