In the bowl of a stand mixer fitted with the dough hook, combine the yeast and the water on low speed. Mix for a minute or so to dissolve the yeast.
Add the sugar. Mix again for a few seconds, then add about 1/2 cup of the flour. Mix again.
Add the eggs. Increase the speed slightly and mix again. Once the eggs are well incorporated, add 1 more cup of flour. On medium-low speed, work in the flour, then add the oil and salt.
Turn off the machine and add 3 cups of the remaining flour (a total of 4 1/2 cups). At medium speed, continue to work the flour into the dough, shutting the machine off once or twice to scrape down the sides of the bowl.
Let the machine knead the dough for about 15 minutes, again turning the mixer off every few minutes to scrape down the bowl, if necessary, and to let the motor rest (with such a dense dough, the motor can overheat if it runs continuously). After a few minutes, the dough should start to come away from the sides of the bowl, although, with all-purpose flour, it may stick slightly to the bottom. If necessary, add more flour, a tablespoon at a time, stopping the motor each time you do so. In the end, the dough should be firm, smooth, and elastic, and only slightly sticky.
Put the dough into a large oiled bowl, turning to completely coat it with oil. Cover with plastic wrap and let rise until tripled in volume, 1 1/2 to 2 hours.