Oh wow, I am really pleased with this one. It's just as pretty as the other braided danish/bread I made. But whereas the dough of that one was somewhere between a bread and a cake (as befitted a banana bread), this dough is somewhere between a bread and a pastry (as befits an actual danish). I've never made a real laminated dough, but this was easy enough that there may be croissants in the future.
1 T yeast
1/4 c warm water
4 T white sugar
2 T brown sugar
1/2 c milk
1/2 t vanilla
at least 3.5 c all-purpose flour
1 stick salted butter, softened
4 oz spreadable cream cheese
Combine yeast and water in the Kitchenaid bowl, and let sit for a minute until the yeast is visibly active. Add the sugars and wet ingredients and stir to combine. Dump in 2.5 c of the flour, put on the dough hook, and knead for 4 minutes. Dump in that whole stick of softened butter, and knead with the dough hook for another 6 minutes, scraping down the sides occasionally. Scrape the dough (which will be barely firmer than muffin batter, although definitely more elastic) onto a surface that has been covered with a layer of some of that remaining cup of flour. Knead by hand as best you can, incorporating up to 1/2 c flour. Place the dough in a large greased bowl, cover with a plastic bag, and let rise until doubled (this will take longer than usual, eg more than 2 hours on a fairly warm day, because the yeast has to be pushing around so much fat). You'll notice we haven't used the cream cheese yet; don't worry, we're getting there.
3 oz cream cheese
2 T white flour
1 T white sugar
2 T greek yogurt
1 T honey
zest and half the juice from 1 large Meyer lemon
~1/3 c mulled fig jam
Stir together everything except the fig jam until smooth, and set aside until ready to spread on the dough.
Flour your surface again, and get out the rolling pin and some parchment paper. Turn the dough onto the floured surface, and roll or press it into a 1 foot square. Now's the time for that 4oz of cream cheese—spread it evenly over the whole surface of the dough. Fold the dough in thirds like a letter, then fold it in thirds the other way, to make a square 1/9 as large and 9 times as tall as your original square of dough. (The thin cream cheese layers between the layers of dough will make the final pastry flakier than your average bread, but not as flaky as more traditional laminated doughs like croissants.) Roll this square into a large rectangle ~10" wide and as long as it gets. (If your rectangle is larger than you want your loaf to be, cut off some of the dough and make it into a second loaf afterward.)
Transfer the dough onto the parchment-lined baking sheet. Spread the cream cheese filling in the long strip down the middle third of the dough, then spread and/or dollop the fig jam over the cream cheese. Form into a "braid" as described previously.
Let rise for an hour or so, then bake at 375F for 25 minutes.