This recipe is based on David Lebovitz's recipe, using milk instead of water, and with the butter incorporation method taken from the Pie & Pastry Bible's approach to croissant/puff pastry/danish dough. (This method of keeping the butter/sugar separate is actually a lot less messy than other recipes I've tried, too, which was nice.)
1 tbsp active dry yeast
3/4 cup (175 ml) milk, microwaved to warm it up (~110F)
260 g unbleached all-purpose flour
1/2 tsp kosher salt
200 g sugar
1/2 a brick of Salted (yes, salted) Plugra (4 oz), plus 2 tbsp salted butter
1. Proof the yeast for ~10 min in a small bowl by mixing with 4 tbps warm milk and a pinch of the sugar.
2. Reserve 1 tbsp flour, putting the rest of the flour and the salt in your stand mixer. Then add the yeast mixture and the rest of the milk.
3. Mix on low speed until the ingredients are wet, then raise speed to medium (#4 on my Kitchenaid) and mix for four to five minutes. The dough should be silky smooth and have cleaned the bowl, but will cling to your fingers.
4. Use a spatula to lightly butter a small bowl. Scrape the dough into the bowl, cover, and allow it to ferment at room temp for 30 minutes. Then let it rest in the fridge for 1 hour.
5. Place half the reserved tbsp flour on a piece of plastic wrap, set the Plugra on it, and then top with the remaining flour. Use the plastic wrap to knead the flour into the butter with your knuckles. Shape the butter into a square, about 5" square and 1/4" thick. It should be firm but malleable.
6. Flour the counter and rub a little flour into the dough. Roll the dough out to a square, then roll the corners out into flaps. Place the butter packet in the center (unlike the Lebovitz recipe, do NOT add sugar to the butter), then fold over the flaps to make the butter packet. Wrap in plastic and let it rest in the fridge for 20 minutes.
7. Gently roll the dough out on a floured counter to about 7" x 14". Sprinkle with 1/4 cup of the sugar, press lightly to adhere the sugar to the surface, and give it a business letter fold with the sugar trapped inside. Brush off excess flour, wrap in plastic wrap, and refrigerate for 20 minutes. (This is the first 'turn'.)
8. Do step 7 two more times, for a total of 3 turns.
9. Butter a 9" round cake pan. After the 20 minute rest from the last turn is done, gently roll it out to a 9" circle and transfer to the cake pan.
10. Preheat the oven to 425 with a rack on the bottom shelf. While the oven heats up, let the cake proof in a warm place (I only gave it 30 min to proof, it could probably have used a full hour).
11. Melt the remaining 2 tbsp salted butter. Sprinkle the top of the cake with the remaining sugar, then drizzle on the melted butter.
12. Bake until the top is caramelized. (I lost track of time, it was about 30 minutes. I also lowered the temp to 400 after about 20 minutes, but after seeing the final result I think this wasn't necessary.) Remove from oven and transfer to a cooling rack.
Using raw sugar instead of cane sugar was a good suggestion from Dobra at the foodie gathering.
Keeping the corner edge from burning while still getting caramelization of the top/bottom can be tricky.
Slashing the top makes for interesting patterns, but distributed the caramel bits oddly. I think I like it without.
Unlike normal croissant dough, letting this sit for a long time to ferment isn't good. The sugar causes a bunch of water to osmose out of the dough, resulting in a sticky mess. It might improve the flavor to do an overnight ferment before incorporating the butter, however.
Similarly, only letting it chill for 20 minutes kept the butter from getting hard and breaking through the dough layers.
I have some photos that I took that I need to upload, but here's a shot of the finished item someone else got: