In the bowl of a stand mixer fitted with the flat beater attachment, combine the milk, yeast, eggs, sugar, vanilla, and salt.
Add the flour to the wet ingredients. Mix the dough on the lowest setting until just combined, less than 30 seconds.
With the mixer running on low speed, add the butter 1 tablespoon at a time, waiting until each piece is incorporated before adding the next.
Once the butter is incorporated, switch to the dough hook. Knead the dough on medium-low speed for 6 to 8 minutes, until it’s smooth and elastic.
Transfer the dough to a lightly greased bowl and cover with plastic wrap. Allow the dough to rise for 2 to 2 ½ hours, or until doubled in size.
Grease two 9" x 4" small Pullman loaf pans.
Transfer the dough to a lightly floured surface and divide in half.
Roll the dough into a 12" square. Dot the dough with half of the frangipane and spread it out evenly.
Add ½ cup plum preserves on top of the frangipane layer and spread it evenly.
Form the babka by rolling up the dough into a log, enclosing the filling.
Slice down the center of the log to cut it in half. Turn the halves cut side up, place side by side, and twist together.
Transfer the twisted loaf into one of the prepared pans.
Repeat the process with the remaining dough and filling.
Cover the loaves loosely with plastic wrap and let them rise for 1 to 2 hours.
Preheat the oven to 350°F with a rack in the middle.
Bake for 30 to 35 minutes, until the tops are deep golden-brown.
Tent loosely with foil and continue to bake for 10 to 15 minutes, or until the babkas reach an internal temperature of 190°F.
Remove the babkas from the oven and transfer them to a cooling rack.
In a small saucepan over medium heat, combine the preserves and water and bring to a simmer.
Brush the glaze evenly over the warm babkas.
Allow the babkas to cool completely before slicing and serving.
