For the dough: In a large bowl or stand mixer, combine 1/3 cup sugar, yeast, and oil with warm water until dissolved. Cover and let stand in warm place for 15 minutes. (I turned my oven on to warm (170 degrees F), turned it off, then put the bowl inside and set the timer.) Sift your flour while you wait.
After the 15 minutes, remove the bowl from the oven and preheat the oven to 425 degrees F.
Beat eggs into yeast mixture. Add salt to sifted flour, then gradually add to yeast mixture to make a very soft dough. Resist the urge to add more flour.
Knead dough for 5 minutes on lightly floured surface, or switch to the dough hook on your mixer and let a machine do the work.
On a well floured surface, roll dough into rectangular shape, about 1/4 inch thick. Mine was about 14x17 inches.
Spread dough with about 1/4 cup soft butter.
Meanwhile, make the almond topping. In a medium pot over medium heat, combine 12 tablespoons butter, 2/3 cup sugar, 6 tablespoons honey, cream, and 1/2 teaspoon kosher salt. Bring to a simmer and then set a timer for about 3 minutes. If the mixture has turned a shade darker, then it is done, otherwise cook up to 5 minutes. It should eventually turn from yellow to light beige. Stir in the the sliced almonds and remove from heat.
Spread about half this mixture on the rectangle of dough, on top of the butter. Roll it up the long way.
Use a super sharp serrated knife to slice into 12 equal rolls. The dough rises so fast, you need to hurry! You can see in the photos that my rolls are a little Jabba the Hut looking. Just do your best.
Spread the remaining almond mixture on top of the shaped rolls.
If your dough isn't looking super puffy, let the rolls rest for 10 minutes. If they are already looking massive, then throw them in the oven at 425. This will depend on how speedy you are. I was slow (taking photos and all) so I put them straight in. You can see how puffy they were in the photos.
Bake for 14-17 minutes or until they are very brown on top. The almonds should be just on the edge of burning (make sure you check it a lot!) See photos. This recipe is easy to under bake, so don't burn your rolls, but don't take them out too early either.
Make the glaze: Combine all ingredients with a whisk. If you're butter isn't soft enough just stick it in the microwave for a few seconds.
Drizzle the glaze over the rolls and serve hot! With a great deal of milk.