Combine water, sugar, and yeast in a small bowl. Let stand for 10-12 minutes or until bubbly.
In a large mixing bowl, combine flour and salt. Pour in the yeast mixture and the olive oil.
If using a stand mixer, process until a smooth ball of dough forms. If mixing by hand, knead for 5 to 8 minutes until smooth and elastic.
Place dough in a greased bowl, cover, and let rise until doubled in size, 1 to 2 hours.
Roll out the dough to ½-inch thickness.
Cut out rounds using a 3-inch cookie cutter.
If cooking all muffins at once, lay them on a cold griddle, cover, and let rest for 1 hour. Preheat oven to 350°F.
Cook muffins over medium-low heat for 7-9 minutes per side until golden brown. If needed, finish in the oven for 10 minutes.
If cooking in batches, place muffins on a cornmeal-dusted baking sheet to rise, then transfer to the griddle and cook as above.
