Whisk together warm water, yeast and 1/2 teaspoon of sugar to activate the yeast; wait 5 minutes until it bubbles.
Add 1 egg, vanilla and olive oil to the liquid yeast mixture.
In the bowl of a food processor or stand mixer, add the salt, sugar, cinnamon and 3 cups of flour. Slowly add the liquids to the flour mixture and begin processing until a ball is formed. If needed, add the last cup of flour, ¼ cup at a time.
Dust counter with flour and finish kneading on the counter with a little flour. The dough will be a little sticky.
Oil a large bowl, add dough, cover with dish towel or plastic wrap and let rise for 1 hour. Punch dough down and let it rest for 5 minutes.
Divide dough into 8 balls. Using a rolling pin and your hands, roll each ball into a rectangle, roughly 4-5’ wide and 7-8’ tall. No shame in using a measuring tape or just eye-balling. If the dough gets too warm and hard to work with, simply put it back in the fridge/freeze to chill.
Spread 1 tablespoon of the filling in an even layer over the dough rectangles, leaving about a ½’ bare boarder around the edges. Starting at the long edge nearest you, tightly roll up each rectangle horizontally jelly roll style into a tight log. Pinch ends and seal, dough will be quite soft at this stage, roll log out until a uniformed shape is made; transfer log to freezer. Repeat with the other pieces of dough. Let each log piece chill in freezer, at least 15 minutes (to ease with the babka bun assembly).
Oil a muffin tin (possible to also bake the buns directly on a baking sheet).
To assemble the buns: cut the roll in half lengthwise, leaving the tip of the log intact, so the striations of the dough and filling are visible. Kitchen scissors work best, a pizza cutter or a very sharp knife work as well. You will have 2 long pieces that are connected on one end. With the cut sides facing up, twist both pieces together. To twist, lift the right half over the left half, followed by the left half over the right half and keep repeating making a 2 stranded plait, then press the bottom end together to seal both pieces. Put each twisted piece back in freezer to chill again before forming the buns.
Note: twisting the dough will get messy and jam will ooze out – there’s no way around this but worry not it is part of the process. Just hold the dough together as best you can (the freezer is your best friend here – put the dough back to chill if it gets too difficult to work with.
When ready to assemble the buns, tie each twisted dough into a knot, tucking the two ends of the knot’s underneath itself. Transfer knots to muffin tin and repeat with all the remaining logs. Let rise for an hour.
When ready to bake, pre-heat the oven to 350 degrees. Brush the tops of the buns with the remaining ½ tablespoon of olive oil (can also add any jam that’s falling out to the tops of the buns).
Transfer to oven and bake for 18-22 minutes, until lightly golden brown.