Lightly butter an 8×4-inch loaf pan. Line with parchment with a 2-inch overhang on the long sides.
Turn out chilled dough onto a clean lightly floured surface. Roll out to a 16x12" rectangle with a short side facing you.
Spread the chocolate filling over the rolled-out dough. Sprinkle the pistachios over the chocolate.
Starting at the short side closest to you, roll the dough into a tight coil, and pinch the seam to seal.
Using a bench scraper or a sharp knife, cut the roll in half lengthwise. Turn the pieces so that the cut side is facing up.
Pinch two of the end pieces together. Twist the halves together, keeping the cut sides facing up, and tuck the ends under. Gently place in a prepared loaf pan.
Loosely cover the pans and let rise in a warm place for 45 minutes or until risen to the edge of the pan.
Preheat the oven to 350F.
Bake babka loaf, rotating pan halfway through, until deep golden brown, 40-45 minutes. If the bread is getting too dark, cover with aluminum foil to prevent burning. The internal temperature should read 190F when fully baked.
While the babka bakes, make the sugar syrup by combining the water and sugar in a small saucepan.
Bring to a simmer over medium heat, stirring until the sugar is fully dissolved. Remove from the heat.
Brush the loaf with the syrup immediately after removing from the oven. Let the babka cool for 30 minutes in the pan. Serve warm or at room temperature.