Use a sharp knife and slice the top and bottom 1-2cm off the eggplant, so that it can stand upright on a chopping board. Carefully slice eggplant lengthways into 10-12 long 0.5cm-thick slices – try to keep the slices of equal thickness.
Mix olive oil, garlic and rosemary and brush onto eggplant slices. Season with salt and pepper. Grill on a preheated BBQ grill plate or in a grill pan until lightly browned, about 5 minutes on each side. The eggplant slices should be cooked through, and soft and pliable. Alternatively, you can bake them on a baking tray lined with baking paper, in a 180degC/360 Fahrenheit oven for about 15 minutes until lightly browned.
To assemble, lay a slice of grilled eggplant on a flat surface and top with a slice of feta, slices of capsicum, and 1-2 basil leaves, then roll up tightly and arrange on a platter, with the seam side down. Repeat with remaining ingredients.