The only recipe I found was a recipe in progress.

HOUSTON'S RESTAURANT COPY CAT VEGGIE BURGERS
Source: AnnaCG
Makes 4 burgers

This is a recipe I am slowly trying to clone. So far, this is the closest I've come. I'm not so sure Houston's uses an egg white, but I added one to help bind the mixture together. Also, the cheese is optional. Houston's definitely grills their buns in butter, so that's probably another reason why their burgers are so good.

4 tablespoons hickory barbecue sauce
1 tablespoon molasses
1 (15 ounce) can black beans, drained
2 cups cooked brown rice
1 tablespoon oat bran
2 tablespoons onions, finely chopped
1 tablespoon finely chopped canned beets
1 teaspoon beet juice
1 teaspoon chili powder
1/4 teaspoon ground cumin
1/4 teaspoon black pepper
1 teaspoon kosher salt
1 tablespoon pickled jalapeno peppers, chopped
1 egg white
2 teaspoons olive oil
4 slices monterey jack cheese (optional)

Stir together barbecue sauce and molasses. Set aside.

In a large bowl, mash beans. Stir in 3 tablespoons of the barbecue mixture (reserving remaining for brushing) and remaining ingredients -- rice through egg white. Form into four 6 oz patties.

Heat olive oil in a cast iron or non-stick skillet over medium. Grill burgers for 2 minutes on one side. Turn and brush with remaining barbecue/molasses mixture. Top with Monterey Jack and grill for another 2 minutes or until cheese is melted.

Serve with lettuce, tomatoes, pickles, onions and mustard on a bun which has been grilled in butter.

Notes:

I have tried a similar recipe and asked Houston's. They do use small black beans, beet juice only-no chopped beets (though that is a nice addition),sweet soy sauce, oat bran, and mushrooms.If you look at Bandera's recipe they use sweet potatoes too. I tried it and its good.I don't think they use egg white-according to Peta's website this burger is vegan. I'm experimenting again tonight. I'll let you know how it comes out.

This may be IT. I've been trying to "reverse engineer" this burer for some time. Two amall differences however, our local Houstons in SOCAL uses small black beans instead of pintos and a small amount of something red like maybe shredded cooked beets to give the burger a rare meat look. The proportions and measurements are kinda weird, and I agree that it needs experimentation.

Houston's do use chopped beets. I used to make the veggie burgers when I worked prep there. Brown rice, oat cereal, chopped black beans, salt, pepper, fresh garlic, jalapenos, white onion. The glaze is honey, soy, hoisin, and molasses. it gets dipped before grilling and held in the marinade before cooking.