Put the flour, sugar, salt, and yeast in the bowl of a stand mixer fitted with the dough hook and mix on low speed until combined. With the mixer running, slowly stream in the water. If the dough seems dry at this point, add a bit more water, a teaspoon at a time, until the dough just comes together. Increase the mixer speed to medium and mix the dough for 10 to 12 minutes, until uniform and smooth.

Transfer the dough to a lightly oiled bowl, cover with plastic wrap, and let rise until doubled in size, about 40 minutes.

Pour the oil onto a rimmed baking sheet and spread it evenly. Turn the dough out onto the oiled pan and use a knife to cut it into 24 equal pieces about the size of a gold ball.

To shape the dough, stretch one-quarter of one piece of dough out, over, and into the center of the dough ball. Do this three more times, working your way around the dough--think of creating a little parachute with the dough where the four quarters meet at the middle. Make a ring by connecting the thumb and forefinger of one hand. Take the dough ball and, smooth top side first, push it through the ring, which will slightly stretch the surface of the dough, tightening the ball. Pinch the bottom of the ball closed. Coat both sides of the ball with a bit more oil from the baking sheet and place it seam side down on the sheet. Continue to shape the rest of the dough balls.

Heat a large nonstick skillet over medium-high heat. Lightly oil a clean work surface.

Set a dough ball on the oiled work surface and, using your hands and a rolling pin, stretch and flatten it into a 12- to 14-inch paper-thin round (try not to make any holes, but if it happens, it’s okay). Carefully lift the dough and lay it in the hot pan. You'll have a few seconds to reposition any folds or creases, but don't worry if it's not perfectly flat. Immediately start stretching your next layer. Once the dough in the skillet starts to brown lightly on the bottom, use a spatula to carefully flip it over. Lay the second stretched dough round directly on top of the first and immediately start stretching your next piece of dough.

When the bottom of the dough in the pan is lightly golden, 2 to 3 minutes, flip the two layers over. Lay the third round of stretched dough on top of the stack.

Repeat this process of stretching, flipping, and adding to the dough stack until all of the layers are stacked in the skillet, like a giant crepe cake. If after you've stacked a dozen or so layers the stack becomes too difficult to flip as one, set that stack aside and start fresh with the rest of your dough. Adjust the heat as necessary while you work so that the layers don't take on too much color. Remove the stack from the skillet and place on a large plate or serving dish.

Serve the mufleta immediately. To eat, each person should peel away a layer of mufleta from the stack, drizzle it with butter and honey, and roll it into a cylinder or fold into quarters.