The appeal of diminutive buns, baked in mini-muffin tins, is not just that you can eat more than one with impunity. Unlike their bigger cousins, they are irresistibly crunchy all around the sides.
Make dough: Stir together yeast and warm water in a small bowl; let stand until foamy, about 5 minutes.
In the bowl of a standing mixer fitted with the whisk attachment, mix milk, butter, eggs, sugar, salt, and vanilla on low speed until eggs and milk are combined, 2 minutes. Add yeast mixture; mix 1 minute. Add 4 cups flour; mix until smooth.
Switch to the dough hook; continue mixing, and add more flour, 1/2 cup at a time, just until dough no longer sticks to bowl (about 2 more cups). Beat dough on medium-high speed, 10 minutes.
On a lightly floured work surface, knead the dough until very smooth, about 2 minutes; transfer to a large buttered bowl. Cover dough with a clean kitchen towel; let rise until doubled in bulk, about 1 hour.
Make topping: Melt butter in a saucepan; stir in sugars and corn syrup. Cook, stirring, over low heat, until sugar dissolves, about 5 minutes. Set aside.
Punch down dough, then turn out onto a lightly floured work surface. Divide dough into three equal pieces; roll each into a ball. (Work with one ball at a time; refrigerate or freeze any not being used.)
Assemble buns: Roll out dough ball into a 7-by-19-inch rectangle; halve lengthwise. Brush each rectangle with 1/2 tablespoon melted butter. Top with filling; leave a 1/2-inch border. Starting on one long side, roll dough into a log. To seal, pinch dough edge to log. Cut the log into 24 slices (3/4-inch-thick).
For each batch, divide 1 cup topping among four (12-cup) mini-muffin tins. Transfer buns to tins.
Preheat oven to 375 degrees, with rack on lower level. Set a wire rack over a baking sheet; set aside. Let buns rise in a warm place until doubled in bulk, about 30 minutes. Bake buns, rotating pan halfway through, until golden brown and bubbling, 15 to 20 minutes. Immediately invert buns onto rack. Serve warm.
Use a variety of baking pans for buns that suit different occasions (and appetites).