Line a large baking sheet with parchment paper. Sprinkle the cornmeal over the parchment paper and set aside.
Place 2 1/2 cups flour in a large mixing bowl. Make a well.
Pour water and 2 tablespoons oil into well. Sprinkle yeast and salt over the water.
Stir dough together with a spoon. (Dough will be ragged.)
Turn dough out onto a floured surface. Add 1/4 cup flour.
Knead dough for 6-8 minutes, adding very small amounts of flour as needed or until dough is smooth, soft and springs back from the touch.
Drizzle a small amount of olive oil into the mixing bowl and place dough in bowl. Turn dough so that it's covered with oil.
Cover with a clean kitchen towel and place in a warm place to rise for 60-90 minutes or until doubled in size.
Meanwhile, prepare artichoke combination: Combine artichoke hearts, rosemary, garlic, 3 tablespoons olive oil and salt to taste in a bowl. Set aside.
When the dough has doubled in size, cut the dough into four even pieces.
On a floured surface, roll each piece into a 6 to 7-inch circle and place on the prepared baking sheet.
Create a few "dimples" with your finger.
Sprinkle each circle evenly with Parmesan cheese.
Place even amounts of the artichoke combination on each of the circles, gently pressing it into the dough.
Cover with the towel and let rise again another 30 minutes.
Preheat oven to 375 degrees.
Bake for 25-30 minutes.
Sprinkle with coarse sea salt. Serve, dipped in good extra-virgin olive oil or other seasoned olive oil.