In a large bowl, whisk together flour, yeast, granulated sugar, and salt. Add warm milk, melted butter, and egg; stir to form a shaggy dough. Knead on a floured surface for 5-6 minutes until smooth and elastic. Place in a greased bowl, cover, and let rise until doubled, 60-75 minutes.

Punch down the dough and roll it into a 12x16-inch rectangle. Spread the 1/2 cup Biscoff over the dough, leaving a 1-inch border on the top long edge. Sprinkle with brown sugar and cinnamon, press lightly, then roll up tightly from the long edge. Cut into 12 rolls and place cut-side down in a greased 9x13-inch pan. Cover and let rise until puffy, 30-45 minutes.

Preheat oven to 350°F (175°C). Bake rolls until golden and bubbling, 22-26 minutes. Cool in the pan for 10 minutes.

Beat cream cheese until smooth. Mix in melted Biscoff, powdered sugar, vanilla, and 1 tbsp milk, adding more milk as needed for a spreadable consistency. Frost the warm rolls and serve.