Finely chop 3/4 cup of the pickled jalapeños. (Any extra slices can be used for other purposes)
In the bowl of a stand mixer, combine the flour, cornmeal, sugar, salt, and yeast.
Add the water and butter, mixing until homogenous. Use the dough hook with the mixer at medium-low speed.
Knead until the dough is smooth — about 9 minutes at medium speed. ** DO NOT leave the mixer unattended! It will walk off the counter! I recommend putting the mixer on a folded towel on the floor. **
Mix in the jalapeños and cheese (both grated and cubed). Knead for another 3 minutes at medium speed.