Warm the milk: Heat the milk to about 110°F, just warm to the touch. Pour it into a large bowl and whisk in the yeast and honey.
Proof the yeast: Let the milk mixture sit undisturbed for 5 to 8 minutes, until it turns foamy on top. This tells you the yeast is active and ready to use.
Mix the dough: Add the egg, salt, 3 tablespoons of melted butter and the bread flour to the yeast mixture. Stir until a shaggy dough forms.
Knead until smooth: Knead the dough on a floured surface for about 8 minutes, or 5 minutes in a stand mixer with a dough hook, until it feels smooth and elastic.
First rise: Place the dough in a greased bowl, cover with a towel, and let it rise in a warm spot for about 1 hour, until doubled in size.
Divide the dough: Punch down the dough and divide it into 12 equal pieces. Roll each piece into a tight, smooth ball.
Arrange in the pan: Place the rolls in a greased 9x13-inch baking dish, sides just touching, so they rise and bake together.
Second rise: Cover the shaped rolls loosely and let them rise again for about 30 minutes, until puffy and nearly doubled.
Bake the rolls: Bake at 375°F for 18 to 22 minutes, until the tops turn deep golden brown and the rolls sound hollow when tapped.
Make the garlic butter: While the rolls bake, melt the remaining 3 tablespoons of butter with the minced garlic and parsley in a small saucepan over low heat.
Brush and serve: Brush the warm garlic butter generously over the rolls as soon as they come out of the oven. Sprinkle with flaky salt and serve warm.