Bring a large pot of lightly salted water to a boil. Add halved brussels sprouts and let cook for 7 minutes. Drain sprouts and wrap them in a clean kitchen towel to dry as much as possible.
Pour canola oil in a deep pot so it's about 2" deep and heat to between 365-400 degrees.
While oil is heating, mix flour, cornmeal, salt, and cayenne in a large bowl. Stir in egg and beer.
When oil is hot, work in batches to dunk sprouts in batter and carefully drop in the oil. Let fry for about 4 minutes, until they're golden brown. You'll likely have to adjust burner level to keep oil temperature in the right range. When sprouts are golden, remove from oil and place in a paper towel-lined bowl. Continue until all sprouts are fried.