1. To make the dough by hand: Begin by making a sponge. In a medium bowl, dissolve the yeast in ¼ cup of the warm water. Add the rye flour and stir with a wooden spoon or rubber spatula to combine. Cover with plastic wrap and let rise in a warm place for 20 to 30 minutes. Add the remaining ½ cup plus 1 tablespoon warm water, the 2 tablespoons olive oil, salt, and 1¾ cups all-purpose flour to the sponge. Using a wooden spoon, mix the dough, incorporating as much of the flour as possible. Turn the dough out on a lightly floured work surface and knead until soh and elastic, 10 to 12 minutes. It will still be a little sticky but shouldn’t stick to your hands. Add only a minimum amount of flour to the work surface to keep the dough from sticking. Generously oil a large bowl. Add the dough and turn to coat on all sides. Cover the bowl with plastic wrap and then place a clean, damp kitchen towel over the top.

To make the dough using a mixer: Fit a heavy-duty stand mixer with the dough hook attachment. In the mixer bowl, stir the yeast into ¼ cup of the warm water. Add the rye flour and mix on low speed until combined. Place a clean, damp kitchen towel over the mixer to cover the bowl and let the sponge rise for 20 minutes. Add the remaining ½ cup plus 1 tablespoon warm water, the 2 tablespoons olive oil, salt, and 1¾ cups all-purpose flour to the sponge. Mix on low speed until the flour is incorporated and the dough gathers together to form a coarse ball, about 3 minutes. Let rest for 2 minutes and then mix on medium-low speed until the dough is smooth and slightly sticky, about 3 minutes longer. Even if the dough seems too sticky, turn the dough out on a well-floured work surface and knead for a minute or two until it forms a smooth ball, adding up to 2 tablespoons of additional flour, if necessary. Generously oil a large bowl (or use the mixer bowl), add the dough, and turn to coat on all sides. Cover the bowl with plastic wrap and then place a clean, damp kitchen towel over the top.

2. Set the bowl in a warm spot (a pilot-heated oven is a good spot, or an electric oven turned to 150°F for S minutes and then turned off). Let the dough rise until doubled in volume, about 2 hours. Punch down the dough, cover it, and let it rise for another 40 minutes. The dough is now ready to be rolled out. (If you want to make the pizza dough ahead, after the first rising, the dough can be punched down and placed in a large lock-top plastic freezer bag. Refrigerate the dough for up to 12 hours. Bring the dough to room temperature before completing the final rise. Alternatively, freeze the dough for up to 3 months. Thaw overnight in the refrigerator and then bring the dough to room temperature before completing the final rise.)