Add flour, sugar, and yeast to the bowl of a stand mixer fitted with a dough hook. Mix until combined on low speed.
Add eggs, mixing for 30 seconds after each. Add water.
Add butter one tablespoon at a time. Add salt and scrape down sides.
Turn speed to medium and mix for 10 minutes until dough is smooth.
Coat large bowl with nonstick spray. Place dough inside. Place tea towel or plastic wrap on top and let rise at room temperature until doubled (up to 8 hours).
Spray two 9" x 4" loaf pans. Line bottoms with parchment paper. Set aside.
Flour baking sheet. Set aside.
Sprinkle counter with flour. Cut dough into two halves and roll first into 10x12" rectangle.
Make chocolate filling (see instructions below).
Spread filling on top of the dough, leaving a 1/4" to 1/2" border.
Wet top of the dough with water and roll from bottom to top to form a tight log.
Place log on floured baking sheet and place in freezer Repeat with other half of dough.
Remove first log from freezer and slice in half lengthwise. Pinch the top of each half together and wind the two halves around each other, keeping the filling on the outside. Tuck the twist inside the loaf pan. Repeat with other log.
Place a tea towel on top of each loaf pan and let dough rise for 90 minutes.
Preheat oven to 375°F. Bake loaves for 30 minutes.
Make the simple syrup (see instructions below).
Remove babka from oven. Brush each with one half of the sugar syrup. Let cool.