Set out all of the butter you'll need for this recipe so it can get room temperature. Pre-heat your oven to 100°F [if your oven doesn't go that low, put it on the lowest setting and then shut it off once it reaches about 100-125 degrees].

For the bread, pour the milk, water, oil, & butter in a large (at least 2-cup) cup measure and microwave for 2 minutes.

In the large bowl of your stand mixer, combine 1 1/2 cups of the flour with the yeast, sugar, and salt.

Crack the eggs into the microwaved liquid, then pour the liquid into the bowl of dry ingredients and mix on low. Add the remaining flour a cup at a time and mix for about four minutes. It is a super liquidy, gooey mess of a dough (honestly, somewhere between batter and dough). You can add a little more flour, though you don't need to; I added maybe an extra 1/4 cup, but you don't want it to be dry later on.

Turn off the oven & open the door. Grease another large bowl (preferably with tall sides) and use a spatula to scrape the dough down the sides of the bowl, then pour the dough into the greased bowl. Lay a towel over the dough bowl and place it in the warm oven, close the door and let the dough rise for an hour.

After an hour, remove the dough from the oven and turn it out onto a *heavily* floured surface. I was scared by how liquidy the dough was, but I added a bunch of flour as I started to work it, and it was a magical texture. Knead the dough to make it more manageable & then roll it out to about a 12" x 20" rectangle.

In a small bowl, mix the softened butter with the orange extract and spread it onto the surface of the dough. Carefully roll up the rectangle short-wise (from the 12" end), trying to keep it 12" wide as you roll. Slice the resulting roll into 1" wide sections, I'd recommend using a pizza cutter or something because when I tried to use a knife I butchered it.

Grease & flour a 12 cup muffin tin or a 9x13 pan and place each roll, spiral/cut side up, into the pan. Cover with a towel & place in the oven to rise for 30 minutes.

Remove the towel (important if you don't want to burn down your house) but leave the rolls in the oven and turn the oven on to 400 F. Bake until the edges begin to brown, about 14-16 minutes (depends entirely on your oven). Remove the rolls from the pan & let them cool on a large platter or a couple of large plates.

When the rolls have cooled a little, make the glaze. Combine the brown sugar, butter, honey, and orange extract in a saucepan over medium-high heat, stirring constantly. Make sure you use silicone or similar, not plastic since it can melt. Add the cream and vanilla, and bring the mixture to a boil for at least two minutes (continue to stir). Remove from the heat and let it cool for a minute or two.

One at a time, hold the rolls by their bottoms and dip the tops into the pot of caramel glaze, swirling around a little to get the top totally covered, then return to the platter. Spoon the remaining glaze over the rolls. Let the rolls sit for about 30 minutes to an hour to let the glaze sink in, then make the icing.

For the icing, combine the very soft butter, powdered sugar, and orange extract with the back of a spoon. Mix a tiny bit (a teaspoon or two) of water into the mixture, and increase a little bit if necessary. You want an icing that's pourable, but not too thin. Drizzle the icing onto the rolls and serve warm (10-15 seconds in the microwave does wonders for leftovers).