Mix 1/2 cup lukewarm water and yeast together in a bowl. Let stand until yeast softens and begins to form a creamy foam, about 5 minutes.
Combine 1/2 cup water, olive oil, honey, and salt in a separate bowl; add 1 cup flour and mix well. Mix yeast mixture into flour mixture. Add remaining flour, 1 cup at a time, until dough is well combined.
Knead dough on a floured work surface until dough is soft, smooth, and elastic, about 8 minutes. Roll dough into 4 calzone shapes.