Mix the warm water and honey in a liquid measuring cup until the honey dissolves. Sprinkle with the yeast and let the mixture stand until foamy, about 5 minutes. Meanwhile, using a food processor, pulse the flour and salt to mix.
Pour the yeast mixture and 2 tablespoons EVOO over the flour mixture. Process until the dough comes together in a sticky ball, about 20 to 30 seconds.
Turn out the dough onto a floured work surface and knead, using the heel of your hand, until smooth and elastic, about 5 minutes.
Lightly oil a large bowl; add the dough, turning to coat. Cover the bowl tightly with plastic wrap. Let the dough stand in a warm, draft-free area until doubled in size, about 1 hour.
Punch the dough down, then turn onto a cutting board. Using a knife, quarter the dough.
Shape 1 dough wedge roughly into a ball. Place the dough ball on the work surface and cup your hand lightly over it. Rotate your hand counterclockwise, letting the dough roll on the work surface. Continue until the surface of the dough is smooth. Repeat with the remaining dough wedges.
Place each dough ball in a large resealable plastic bag or plastic container with a lid. Refrigerate for 10 to 48 hours (the dough will continue to rise). Let the dough sit at room temperature for 1 hour before shaping, or freeze for up to 2 weeks. Let the frozen dough sit at room temperature for 2 hours before shaping.
Turn out 1 ball of dough onto a lightly floured work surface. Press it out on the work surface into a 9-inch round, a long rectangle or an oval. Repeat with the remaining dough balls. To make 3- to 4-inch mini pizzas, cut each dough ball into 4 pieces, then press or stretch into shape.