Combine the milk and water in a 2-cup measuring cup. Warm the mixture in the microwave and bring it to 96-105 degrees. (this is the perfect temp to grow the yeast - too hot and it will kill it).
Once the mixture is the perfect temp, whisk in the sugar so it is mostly dissolved.
Sprinkle the yeast over the top. I like to dip a spoon in to push the yeast down in some spots so that it can all get moistened - but not stirred in. This allows it to still float on top so it can grow.
Let the yeast proof for 5-10 minutes. If the yeast does not proof - do not proceed any further. There is a good chance that the yeast is too old or there is another factor keeping it from proofing. The rolls will not rise and turn out right without this crucial step - so this would be a good time to start over if needed before using up the remaining ingredients.
Once the yeast has been proofed - pour it into the bowl of a stand mixer and add the butter and egg.
Use the dough hook to mix together. Then slowly add the flour.
Let the mixer knead the flour to form the dough. It should be somewhat smooth and start to pull away from the sides of the bowl.
Turn it out onto a lightly floured surface. Knead until smooth.
Place it in an oiled bowl. Cover and set it in a warm place to rise for about 90 minutes or until it has doubled in size. I like to set it on a seed germinating pad or a heating pad since we live in North Idaho and it’s usually cold in my kitchen.
While you wait - make the honey butter by whisking together the melted butter and the honey.
Punch down the dough and roll it out on a lightly floured surface. Use a rolling pin to roll it into a ½”-thick rectangle.
Use a biscuit cutter or round cookie cutter to cut circles out of the dough.
For the classic “Parker house look”, indent the middle of the circles.
Brush each circle with the honey butter.
Fold them in half and place them in a greased 9x13 baking dish.
Repeat with any remaining dough. I was able to get TWO 9x13 dishes full of rolls - 36 total.
Cover and let rise in a warm place for 1 hour or until doubled in size.
Preheat the oven to 350 degrees and then bake for 15-20 minutes - or until golden. I like to broil for 1-2 minutes after they have baked to really deepen that color on top.
Once baked, remove and brush with the remaining honey butter and then sprinkle with the flaky sea salt.
Serve immediately while warm.