Simmer milk gently on stovetop, being carefully not to burn or boil. Remove from heat and let cool to lukewarm, about 80-90 degrees.
Mix the milk, yeast, and honey in mixing bowl until well combined. Let sit for 5 minutes.
Add 3 tablespoons of the melted butter, the egg (let egg come to room temp ahead of time works best to not disturb your yeast), salt, and 2 cups of flour. Mix slowly until smooth. (Use a mixer with a dough hook if you have one, otherwise it can be mixed by hand.) Gradually add the remaining 2 cups of flour and mix until dough has formed.
Knead by hand or with dough hook for approximately 8 minutes. Then drop the dough onto a floured surface and gently shape into a mound.
Spray a large bowl lightly with cooking spray and drop the dough inside. Cover the bowl (plastic wrap or a damp cloth works) and let it rise for an hour in a warm place.
Punch down the dough and roll it out on a flat, floured surface until it’s about ½ inch thick. Fold it in half and gently seal.
Cut into 16 squares of even size and place on a lightly greased cookie sheet. Cover them and let them rise for 30-40 minutes, until doubled in size.
Bake in an oven preheated to 350 degrees for 12-15 minutes, or until the tops are a light golden brown. Be careful not to over bake.
Brush the tops with the remaining tablespoon of melted butter.
Mix all ingredients together until creamy for the Texas Roadhouse Copycat Butter. Serve rolls generously slathered with the sweet butter.