Combine flour, sugar, yeast, and salt in a food processor and process until combined, about 3 seconds. With processor running, slowly pour cold water and oil through the food chute and process until dough forms a sticky ball that clears the sides of the bowl, 45 seconds to 1 minute.

Lightly oil a work surface and set dough ball on top; knead until smooth, about 1 minute. Shape dough into a tight ball and place in a large bowl greased with oil. Cover bowl with plastic wrap and allow dough to rise at room temperature until almost doubled in size, 1 hour 30 minutes to 2 hours.

Preheat the oven to 500 degrees F (260 degrees C). Place a pizza stone on the lowest rack in the oven.

Transfer dough to a lightly floured work surface and gently re-shape into a ball. Coat dough ball lightly with flour and flatten into an 8-inch disk using your fingertips. Using a rolling pin, roll dough into a 12‑inch circle, dusting dough lightly with flour as needed.

Dust a pizza peel with cornmeal and transfer dough circle on top. Spread marinara sauce on dough, leaving a 1/2-inch border around the edge. Top evenly with mozzarella, pepperoncini, pepperoni slices, and sliced jalapeño.

Carefully transfer pizza onto pizza stone in the preheated oven and bake until edges are golden brown and cheese is melted, about 10 minutes.