In a small bowl, whisk together yeast and warm milk. Set aside until yeast mixture begins to form a creamy foam, about 5 minutes.
In a large bowl whisk together flour, sugar, and salt. Add yeast mixture, melted butter, and egg. Knead until dough comes together in a ball and no longer sticks to the sides of the bowl. Transfer dough to a greased bowl and cover with a clean damp towel. Set aside to rise for 20 minutes.
1. Process dried figs in food processor until finely chopped. Add softened butter, brown sugar, and cinnamon in the food processor. Pulse until mixture forms a paste.
Turn out dough onto a lightly floured surface. Roll dough out into a large rectangle, approximately 14x9 inches. Spread fig paste over dough. Beginning at the long edge, tightly roll up the dough as you would if you were making cinnamon rolls.
Leaving a 1-inch gap from the top, slice rolled dough in half lengthwise. Carefully turn cut dough centers so that fig layers are facing upwards.
Twist the left strand of dough over the right strand, then continue until the entire dough has been twisted together. Shape twisted strand into a circle, pressing ends together. Transfer to a parchment-lined baking sheet.
Cover with damp towel to rise again while oven is preheating. Preheat oven to 375°F. Whisk together egg and water. Brush danish with egg wash.
Bake danish for 30-35 minutes.
Whisk together cream cheese, softened butter, vanilla, and powdered sugar until smooth. Drizzle over danish, if desired, or simply sprinkle with sifted powdered sugar.