To Make the Brioche Dough: In the bowl of a stand mixer, add the flour, sugar, yeast, egg, egg yolk, and milk. Using the hook attachment, mix on LOW speed for 2-3 minutes. Add the cubed softened butter and knead until a soft and pliable dough, about an additional 3-4 minutes.
Transfer the dough to a greased bowl, cover with saran wrap, and set aside in a warm environment for 1-2 hours, until doubled in size.
Preheat oven to 375F. Line a rimmed baking pan with parchment paper.
Once risen, turn out the dough on a clean surface to divide into 8-12 equal pieces. Roll into tight balls, then set aside while you prep the cream cheese filling.
To Make the Filling: Add the softened cream cheese to the bowl of a stand mixer fitted with the paddle or whisk attachment. Beat for 1-2 minutes, until smooth. Add the powdered sugar, milk, and vanilla bean paste. Beat for 2-3 minutes, until smooth and light.
To Make the Coffee Cake Crumb: Combine all ingredients in a bowl. Mix until crumb-like texture. If it seems too dry, you can add a little olive oil or more melted butter.
To Assemble the Danishes: Press your fingers along to create a little under 1/2" circular edge for each dough ball. Gently stretch out the center until about 1/4" thick. Think of creating a large doughnut with a center that connects it. Place on the prepared baking pan.
Evenly distribute the cream cheese filling between the danishes. Top with the pumpkin butter, about 3-4 tablespoons per danish.
Brush the edges with the beaten egg, then add the coffee cake crumb along the edges and (optional) center.
Bake for 20-30 minutes, rotating the pan halfway through, until edges are deeply golden and centers are set. Let rest at least 10 minutes.
To Make the Glaze: Whisk all ingredients together until smooth. Drizzle on top of the danishes to be enjoyed!