Preheat the oven with grill function to medium-high heat (200°C / 400°F).
In a large bowl, combine minced turkey, finely chopped onion, minced garlic, chopped rosemary, salt, and pepper; mix well.
Divide the mixture into 4 equal portions and form each into a round patty.
Brush all sides of the patties with sunflower oil.
Place patties on a baking sheet and place under the grill; cook for 5 to 6 minutes on the first side.
Flip the patties and grill for another 5 to 6 minutes until the internal temperature reaches 74°C / 165°F.
Cut burger buns in half. Layer lettuce, a cooked patty, cucumber slices, and mayonnaise on each bottom half, then top with the other half. Serve immediately.