Heat the oil in a skillet over medium heat. Add the bread crumbs, garlic and a pinch of salt & pepper. Cook until toasted and browned, stirring frequently - should take about 10 minutes. Turn down the heat if it starts to brown too quickly. Remove from the heat and set aside.
Meanwhile, add all of the dressing ingredients to a blender or food processor. Blend until smooth. Taste and adjust the seasonings as needed. Set aside.
Cut the lettuce into 6 wedges. Cut those wedges in half - you will have 12 lettuce wedges.
To assemble, place the wedges on a platter. Drizzle with the dressing, making sure it gets into all of the crevices. Top with bread crumbs, vegan parmesan and parsley. Serve right away or chill in the fridge.
Video
Notes
I made the bread crumbs from scratch by placing cubed ciabatta bread in a food processor and pulsing.