In your large mixing bowl, combine the warm water, 1 tablespoon of honey, and the yeast. Stir gently and let it sit for 5 to 10 minutes until foamy and bubbly.
Add 3 tablespoons of softened butter, the eggs, salt, and 4 ½ cups of flour to the yeast mixture. Using a wooden spoon or your stand mixer with a dough hook on low, mix until a shaggy dough forms.
Cover the bowl tightly with plastic wrap or a clean kitchen towel. Let the dough rise at room temperature for 1 to 2 hours or until it has doubled in size.
Lightly flour your work surface and turn the dough out. Divide it into 12 to 15 equal pieces. Shape each piece into a smooth ball by folding the edges under and pinching the seams. Place the rolls into a greased baking pan, spaced slightly apart.
Cover the rolls again and let them rise for 45 minutes to 1 hour until puffy and nearly doubled.
Preheat your oven to 375°F (190°C). Bake the rolls for 18 to 22 minutes, or until golden brown on top. Remove from the oven and immediately brush with the remaining melted butter and 2 tablespoons honey mixture.
Allow the rolls to cool slightly before serving warm.
