10 reviews of Burro Cheese Kitchen - CLOSED "This place had excellent food. I ordered the girlled cheese with brisket and a spicy pineapple sauce and I. Burro Cheese Kitchen. likes · 1 talking about this · were here. Artisan grilled cheese sandwich shipping container trailer eatery //. Thrillist Best Grilled Cheese in Austin · Thrillist Burro Part #1 · Thrillist write up #1 was post Waylon & Willie consumption —- > check the full story · Zagat <3.