Whisk 1 cup flour, water, honey, and yeast together in a bowl. Let stand until yeast softens and mixture is bubbly, about 20 minutes.
Stir remaining flour, olive oil, and salt into yeast mixture. Beat mixture in a bowl with an electric mixer fitted with a dough hook attachment, adding more flour as necessary, until a soft and tacky dough forms, 3 to 4 minutes. Place dough in mixing bowl with a little olive oil, cover bowl with a plate, and let rise until doubled in size, 90 minutes.
Punch dough down and transfer to a lightly floured work surface. Divide into 4 balls; cover each and let rest until dough rises slightly, 30 to 45 minutes. Roll into desired shapes and thickness.