Heat the olive oil in a skillet over medium heat. Add the diced onion and sauté for about 3-4 minutes until softened.
Add the plant-based ground meat to the skillet, breaking it apart with a spatula. Cook for about 5 minutes, stirring occasionally, until heated through and slightly browned. Season with salt and pepper to taste.
Prepare the wraps by laying them flat on a clean surface.
Once the plant-based meat is done, divide it evenly among the wraps, placing it in the center of each.
Sprinkle dairy-free cheese shreds over the plant-based meat on each wrap.
Top with sliced tomatoes, shredded lettuce, and pickles.
Drizzle ketchup and mustard over the fillings.
Fold in the sides of each wrap and then roll it up tightly from the bottom to enclose the filling.
Place the wraps seam-side down in the skillet and toast for about 1-2 minutes per side, until golden brown and crispy.
Remove from the skillet, slice in half if desired, and serve with extra condiments on the side.