Brush the avocado halves with olive oil and season with salt and pepper.
Place the avocados on the grill, cut side down, and grill for about 4-5 minutes.
Remove the avocados from the grill and let them cool slightly. Scoop out the flesh and slice.
Warm the tortillas on the grill for about 1 minute on each side.
Assemble the tacos by placing grilled avocado slices on each tortilla, followed by shredded cabbage, cilantro, and a dollop of sour cream. Serve with lime wedges.