In a stand mixer, combine the 3 tablespoons of lukewarm water and yeast. Let it sit until dissolved (about 5 minutes). Mix for about a minute with the mixer. A hand mixer or a mixing spoon will do fine, just take a little more muscle.
Meanwhile, in a medium microwave-safe bowl, combine the milk with the butter, sugar, and salt, and microwave for about a minute. Stir until everything melts.
Lightly whisk in the honey and egg to the butter mixture (if the mixture is too hot, let it cool to lukewarm to prevent the eggs from curdling.
Dump everything into the yeast mixture. Mix for 2 minutes at medium speed.
Add 2 cups of bread flour and mix well. Then add 1½ cups of all-purpose flour, and continue mixing the dough until it doesn't stick to the sides or bottom of the bowl when kneading.
Add just enough flour as needed to make a soft dough. Less is better, and it's better to knead it well instead of adding more flour.
Turn the dough on a lightly floured surface and knead for 8-12 minutes or more for airy bread. Place the dough in a greased bowl, turning once to coat. Cover loosely with a clean cloth and let rise in a warm, draft-free place for 1-2 hours or until doubled.
Punch the dough down, knead briefly, and refrigerate covered for 30 minutes. Divide the dough into 12 equal pieces, shape them into balls, and put them in a greased 12-inch round pan. If baking soon, let them rise until almost doubled. Depending on the weather, it usually takes 30-40 minutes.
You can refrigerate them before baking for up to 24 hours, or let them rise and bake them as soon as they're ready.
Preheat the oven to 350℉ (180℃).
Brush the top of the rolls with melted butter or milk. Bake until the crust is deep golden brown and the bottom of the rolls sounds hollow when tapped, 20-25 minutes.
Remove from the pan and let them cool. I like to eat mine while they're still warm.