Baked corn dogs

1 1/2 cups all-purpose flour (spooned and leveled), plus more for dusting sausages
2/3 cup yellow cornmeal
2 teaspoons baking powder
2 teaspoons sugar
Coarse salt and ground pepper
2/3 cup milk
2 large eggs, lightly beaten
2 teaspoons vegetable oil
4 precooked smoked chicken sausages (13 ounces total)
Ketchup and mustard, for serving (optional)

Preheat oven to 375 degrees.
Line a baking sheet with parchment paper; set aside.
In a medium bowl, whisk together flour, cornmeal, baking powder, sugar, 1/2 teaspoon salt, and 1/4 teaspoon pepper.
Make a well in center; add milk, eggs, and oil.
Mix just until combined.
Insert an ice-pop stick into one end of each sausage, leaving a 1 1/2-inch handle.
Dust with flour; tap off excess.
Using handle, rotate each sausage over bowl as you spoon batter to coat evenly.
Place on sheet; bake 5 minutes.
Remove from oven. Using a spatula, reapply batter that has slipped onto sheet.
Return to oven; bake until golden, 20 minutes.
Serve with ketchup and mustard, if desired.