In a small bowl, mix together yeast, lukewarm milk, and 1 teaspoon sugar. Mix well and leave undisturbed for about 10 minutes until the mixture gets foamy.
In your mixer bowl, whisk together the remaining sugar, flour, and salt.
Add foamy yeast mixture, egg, and vanilla. Attach dough hook, then mix on low until the dough starts to come together, 2–3 minutes.
Increase speed to medium and knead dough until it’s smooth and soft, 5–10 minutes.
Reduce mixer speed to low. Add butter to bowl a cube or two at a time, allowing buttery addition to be fully incorporated before adding the next. NOTE: This will take a few minutes to properly add the butter.
Once butter is fully incorporated, increase mixer speed to medium. Knead dough until very smooth and soft, about 5 minutes.
Tip dough out onto a clean work surface and form into a ball. Lightly grease inside of your mixer bowl with neutral oil. Place dough back into bowl and roll around to coat all sides with oil. Cover bowl with beeswax wrap or cling film and place in a warm, dry spot and leave undisturbed until dough has doubled in bulk, 40–55 minutes.
Grease inside of a 9" springform pan; set aside.
After dough has doubled in size, punch it down to release excess gas build-up. Turn out onto a floured surface and divide dough into 16 equal pieces (about 57g each).
Flatten a dough ball into a 3-inch circle. Spoon about 1 teaspoon pflaumenmus (plum butter) into the centre. Bring edges of dough up over the filling, pinching to seal filling tightly inside. If necessary, massage or shape your bun to make it a little rounder.
Repeat with remaining dough and plum butter until you have 16 buns.
In a bowl, mix together cinnamon and sugar. Brush each bun with melted butter, then roll in cinnamon-sugar. Place buns seam-side down into prepared pan.
Loosely cover springform pan with cling film or a clean dishtowel, and place in a warm, dry spot and leave undisturbed until buns nearly double in size, roughly 30 minutes. NOTE: Wondering if your buns have proofed enough? Give one a wee poke with your finger. If indentation springs back slowly, they’re ready to be baked. If the indentation springs back quickly, buns need to continue proofing.
Heat oven to 375°F.
Bake for 25 minutes or until light golden brown. (Internal temperature should be 190–200°F.)
Once buns are baked, transfer pan to wire rack and allow to cool for 10–15 minutes. When the springform pan is cool enough to touch, remove circle o’ buns from pan.