Add eggs, milk, and beer to large mixing bowl and beat until blended.
Add flours, salt, canola oil, basil, and oregano to bowl with egg mixture and beat on medium until batter is smooth. Scrape sides of bowl midway. You can let the batter sit for an hour, or you can use it right away if desired.
Start heating a 10-inch nonstick crepe pan or skillet over medium heat. Coat it with canola cooking spray. Pour 1/4 cup of batter into the center of the crepe pan and tilt to cover bottom of the pan in a thin layer. Cook the crepe until it is just golden on one side (about 1 minute). Flip it over and cook until other side is golden (about 30 seconds).