Well according to wikipedia I am confusing The Cheesecake Factory with something else. I've never been to one but I thought there was one in a mall when I was on vacation somewhere. Maybe not.
"The Cheesecake Factory offers an upscale casual dining experience, complete with a full bar, whose lavish decor includes limestone floors, decorative columns, hand-painted fabrics, contemporary lighting, and cherry wood trimmings.
Its extensive menu includes over 200 selections, including appetizers, pizza, pasta, seafood, steaks, salads, sandwiches, etc. Its featured dishes include Chicken Madeira, Miso Salmon, Cajun Jambalaya Pasta, and The Factory Burger."
So perhaps Leonard and Sheldon were enjoying BBQ Factory Burgers.