Preheat grill to medium-high heat (or preheat oven to 400 F).
If grilling, grill aubergine slices and pepper quarters (without brushing with oil) until lightly charred, but still moderately firm, turning occasionally. Remove from heat into a bowl and cover with plastic (this will continue to soften the vegetables).
If oven-roasting, place aubergine and peppers on a parchment–lined baking tray and roast for 15 minutes, turning once. Remove from tray into a bowl and cover with plastic (this will continue to soften the vegetables.)
Once cooled for about 10 minutes, slice into bite-size pieces and toss with orange juice and zest, garlic, ginger, sesame seeds and olive oil. Season to taste and spoon into serving dish. Sprinkle with parsley and chill until ready to serve.
Salad is best served at room temperature.