In a medium bowl, stir together ¾ cup (180g) warm milk and yeast. Let stand until mixture is foamy, about 10 minutes.
In the bowl of a stand mixer fitted with the paddle attachment, stir together ⅓ cup (67g) sugar, melted butter, sour cream, egg, vanilla, and remaining ¼ cup (60g) warm milk until combined.
In a large bowl, whisk together flour, salt, ¾ teaspoon (1.5g) cardamom, and cinnamon. Stir 4 cups (500g) flour mixture into sugar mixture. With mixer on low speed, add yeast mixture, beating just until combined. Beat in remaining ½ to ¾ cup (63 to 94g) flour mixture. (Dough should be slightly sticky.) Switch to the dough hook attachment. Beat at low speed until dough is smooth and elastic, 4 to 5 minutes.
Turn out dough onto a lightly floured surface, and shape into a smooth round. Spray a large bowl with cooking spray. Place dough in bowl, turning to grease top. Loosely cover and let rise in a warm, draft-free place (75°F/24°C) until doubled in size, 1 to 1½ hours.
Punch down dough. Refrigerate for 15 to 30 minutes.
Line 2 baking sheets with parchment paper.
Turn out dough onto a lightly floured surface, and roll into a 20x16-inch rectangle. Spread Pear Butter (see instructions below) onto dough, leaving a ½-inch border on short sides. In a small bowl, whisk together egg white and room temperature milk. Brush one border with egg wash. Fold dough in half crosswise, trimming if needed to create a 16x10-inch rectangle. Gently roll over dough to ensure filling is even. Cut dough into 16 (1-inch-wide) strips. Twist each strip, spiral dough, and tuck end under. Place on prepared pans. Cover and let rise in a warm, draft-free place (75°F/24°C) until puffed, about 30 minutes.
Preheat oven to 350°F (180°C).
Brush buns with egg wash. In a small bowl, stir together remaining ¼ cup (50g) sugar and remaining ½ teaspoon (1g) cardamom. Top buns with cardamom sugar.
Bake, one batch at a time, until golden brown and an instant-read thermometer inserted in center registers 190°F (88°C), 20 to 25 minutes. Let cool on pans for 10 minutes. Serve warm, or let cool completely on wire racks. Store in an airtight container at room temperature for up to 3 days.