In a large mixing bowl, combine the lukewarm water and dried yeast. Allow it to sit for about 5-10 minutes, or until it becomes frothy.
In another bowl, whisk together the flour, salt, and sugar.
Once your yeast mixture is frothy, add the flour mixture to the bowl. Follow this with the eggs and melted butter. Mix everything together until a dough begins to form.
Turn the dough out onto a lightly floured surface and knead for about 10 minutes, or until it becomes smooth and elastic.
Place the kneaded dough in a greased bowl, cover it with plastic wrap, and let it rise in a warm spot until it doubles in size, approximately 1-2 hours.
Once the dough has risen, punch it down to release the air. Gently fold in the grated cheddar.
Divide the dough into equal portions (about 12-15 rolls). Shape each piece into a ball and place them on a baking sheet lined with parchment paper.
Cover the shaped rolls with a clean kitchen towel and let them rise again for about 30-45 minutes, or until they have puffed up.
Preheat your oven to 375°F (190°C). Once the rolls have risen, bake them for 20-25 minutes, or until they are golden brown.
Remove the rolls from the oven and let them cool on a wire rack for a few minutes before serving.