Reuben Babka

In the bowl of a stand mixer fitted with the whisk attachment, whisk the warm milk and sugar together. Sprinkle the yeast over the top and let stand until foamy, 5 to 10 minutes.
Add the melted butter and 3 of the eggs, then whisk until well incorporated. Switch to the dough hook, then add the flour and salt. Beginning on low speed and gradually increasing to medium, knead until a smooth, elastic dough forms, about 5 minutes. If the dough is very sticky, add more flour 1 tablespoon at a time.
Slick a medium bowl and your hands with 2 tablespoons of the oil. Using your hands, transfer the dough to the bowl, gently turning to coat it with the oil, and shape it into a smooth ball. Cover with plastic wrap or a clean kitchen towel and set aside in a warm place until doubled in size, 1 hour to 1 hour 40 minutes. (Alternatively, you can let the dough rise in the refrigerator, covered, overnight.)

While the dough is rising, in a medium bowl, stir together the pastrami, cheese, sauerkraut, mayonnaise, ketchup, and mustard until well combined.

Preheat the oven to 350°F (177°C). Slick two 9-by-5 inch (23-by-13 cm) loaf pans with the remaining 2 tablespoons of oil, using 1 tablespoon for each pan.
Divide the dough into 2 equal balls. On a lightly floured surface, roll out one ball of dough into a 12-by-14inch (30-by-35 cm) rectangle, about 1/4 inch (6 mm) thick and aligned horizontally.
Spread half the filling evenly over the surface of the dough, leaving a 1-inch (2.5 cm) border all the way around the rectangle. Starting with the edge closest to you, roll up the dough tightly into a log. Using a serrated knife, carefully cut the roll lengthwise in half. Twist the strands together and pinch the ends to seal. Carefully place the babka in one of the prepared loaf pans.
Repeat this process with the remaining dough and filling. Cover both babkas loosely with plastic wrap or clean kitchen towels and set aside in a warm area until the dough expands to fill the pan, about 45 minutes.

In a small bowl, beat the remaining egg, then liberally brush each babka with the egg and top with caraway seeds. Bake, rotating the pans halfway through, until the babkas are golden and each has reached an internal temperature of 185°F (85°C), 40 to 55 minutes.
☞ TESTER TIP: If your loaves begin to darken too much during baking, cover with foil.
Remove from the oven and let cool slightly in the pans, then remove the loaves from the pans and let cool completely before slicing and serving. Babka is best served the day it’s baked.