The phrase "thick wedges" refers to pieces of food, usually vegetables or potatoes, that are cut into a triangular shape and are larger and chunkier than usual. Full definition
Finally slice the onions into thick wedges as seen above. (grillinfools.com)
Once the beets have cooled, and you've removed the skins, cut them into 1/4 inch thick wedges and set aside in a medium mixing bowl. (biggirlssmallkitchen.com)
While the cauliflower cooks, slice the potato into 1/4 inch / 0.6 cm thick wedges. (veggiesouls.com)