Combine 1 cup flour, 2/3 cup corn meal, 1 tablespoon brown sugar, 1 teaspoon salt, 1 teaspoon baking powder, and 1 teaspoon baking soda in a large mixing bowl and mix well.
Lightly whisk 1 egg and then whisk in 1 cup beer.
Add the liquid mixture to the dry, using the whisk to combine. Transfer the mixture to a tall glass, or as much will fit. It will be easier to dip the veggie “dogs” in to the batter this way.
Cut 2 carrots and 4 broccoli stalks into 1/4″ slices.
Bring a small pot of water to a boil and then reduce it to a simmer. Add the carrot and broccoli slices to the water, cooking for about 2 minutes. It just depends on how tender you want these “corndogs.” I like them a little crunchy, personally. Also, you could add a tablespoon of salt to the boiling water for extra flavor.
Transfer the slices to a colander and let them dry.
Slide the veggies onto a skewer, alternating between the carrots and the broccoli. I want these to have a veggie dog shape so, you can trim them up so they are cylindrical.
Bring enough corn oil for fryng up to 375 degrees F. Dip the “dogs” into the batter, removing any excess and then transfer them to the hot oil. Let them fry until golden brown, then place them on a drying rack.
Enjoy and Happy Super Bowl!