Peel the beets and cut each one into 1-inch wedges. Try to keep the wedges roughly the same size so they cook evenly.
Place the beet wedges in a bowl and toss with the olive oil, salt, black pepper, and dried thyme until every piece is well coated.
Preheat the air fryer to 390 degrees F. Arrange the beet wedges in a single layer in the basket. Air fry for 20 to 25 minutes, shaking the basket every 8 minutes, until the beets are tender when pierced with a fork and the edges are slightly caramelized.
While the beets cook, whisk together the balsamic vinegar and honey in a small bowl to create a quick glaze.
Transfer the roasted beets to a serving plate and drizzle the balsamic-honey glaze over the top. Scatter crumbled goat cheese and chopped fresh parsley over the beets. Serve warm as a side dish or over a bed of mixed greens.