Make a brine by dissolving 1 tablespoon of cooking salt in 4 cups of warm water and let cool down.
Slice eggplant in discs and soak in the brine for 30-60 minutes.
While you wait, heat up your BBQ.
Make pesto with basil, pine nuts, extra virgin olive oil, grated cheese, garlic and lemon juice. You can use a food processor or a mortar and pestle. Season to taste.
Drain eggplant and dry with paper towels.
Spray eggplant with extra virgin olive oil spray (or brush with extra virgin olive oil) on both sides and place on the grill grates. Place capsicums directly on the grill grates. Close the lid.
Turn eggplant and capsicum after 5 minutes.
Remove eggplant after another 5 minutes (i.e. after grilled on both sides), turn capsicums every 5 minutes until the skin should be black on all sides (this should take about 15 minutes).
When capsicum is ready, place in a bowl and cover with cling wrap (the steam will help loosen up the skin).
Lower BBQ heat to the lowest setting.
Cut eggplant discs in bite-sized pieces.
Remove the cling wrap from the capsicum bowl and carefully peel the skin with your hands. Transfer to a chopping board, use a knife to remove stem, membranes and seeds, chop coarsely.
Whisk eggs in a bowl. Season lightly with salt and pepper.
Spray BBQ pan with extra virgin olive oil. Pour eggs, add vegetables, top with crumbled feta. Drizzle 1/2 of the pesto on top.
Place pan in the BBQ and cook with the lid closed until eggs are fully set, about 20 minutes.
Turn off BBQ, remove pan. Let sit for a minute before slicing.
Serve with an extra drizzle of pesto, a side salad and a piece of toast if you want.