In the bowl of a stand mixer add the water, yeast, and a pinch of sugar. Let sit for 10 minutes. You want the yeast to get bubbly and foamy, this signifies the yeast is active and working.
Once the yeast is bubbling add the sugar, salt, and 3 cups of flour. Using the paddle attachment, mix until combined. With mixing speed on low add the eggs one at a time. Add shortening and mix until combined. Switch to the dough hook, add remaining 4 cups of flour. Mix on medium low speed for 8 minutes. The dough should pull away from the sides of the bowl. Dough will be tacky but not overly sticky. If the dough is sticky add additional flour 1 tablespoon at a time until the dough reaches the correct consistency.
Place the dough in a lightly oiled bowl then flip it over so that the top and bottom of the dough are lightly oiled. Cover and let rise for 1 hour or until doubled in size.
When dough has nearly doubled in size punch down, and shape into 24 balls. Place the dough balls on a lightly greased baking sheet. Cover the baking sheet with plastic wrap and let the dough balls rise for 30-40 minutes or until puffy and almost double in size.
Preheat the oven to 400° F. Once the rolls have nearly doubled in size place the rolls in the oven and bake for 12-20 minutes, or until the rolls are golden brown on top and fully baked.
Brush the tops of the warm rolls with butter.
Store rolls in an airtight container. Rolls will keep for 4-5 days at room temperature, but best when eaten the same day they are made. You can't beat fresh rolls!