In a shallow dish, sprinkle strawberries with sugar, cover, and refrigerate overnight.
In a medium saucepan, add strawberries, lemon juice and heat to a simmer.
Stir frequently until jam thickens and bubbles cover the surface(about 30 minutes).
In a food processor, blend the jam until you have a puree-like consistency. Pour jam into a clean jar and let cool completely.
To Make the Dough
In a measuring cup, stir together warm milk and yeast. Let it sit until it becomes foamy, about 10 minutes.
Meanwhile, in a small bowl, whisk together eggs, salt, and sugar.
Add egg mixture, foamy yeast-milk mixture, and flour into a stand mixer. Beat until a shaggy dough forms. Continue to beat on medium until a uniform consistency.
Start adding the butter 1 Tbsp at a time while still beating the dough. Ensure that each addition is incorporated well before adding the next one. After all 6 Tbsp of butter have been added, continue to beat for additional 5 minutes, or until the dough is smooth with an elastic consistency.
Grease a large bowl with oil, and place the dough inside the bowl. Cover with plastic wrap, and refrigerate overnight.
Take the dough out of the fridge and roll out onto a well-floured surface to 10 inches wide and 12 inches long. Trim the sides to create perfect edges if you prefer.
Spread the jam over the dough, leaving a ½-inch border all around the edges. Brush the end farthest away from you with water. Roll the dough into a log. Gently transfer the log to a baking sheet and cover with a plastic wrap. Then, chill for about 30 minutes, so it will be easier to shape in the next steps.
After chilling, gently cut the log lengthwise through the middle. With cut sides up, lay one piece on top of the other to form an X shape..
Working on one side of the X shape, twist the two pieces together twice, still making sure the cut sides are facing up. Repeat the same to the other side of the X shape to get a fat twisted log with the jam layers facing up.
Lightly butter a 9”x5” loaf pan, and lightly sprinkle with flour Place the babka into the pan and cover with a damp towel. Let rise at room temperature 90 minutes, or until doubled in size.
Preheat the oven to 375F. Bake for 25 minutes or until a toothpick in the center comes out clean.
Meanwhile, make the glaze by mixing the jam and water. When the babka is out of the oven, brush the top with the jam mixture. Let cool for 15 minutes at room temperature, and then transfer the babka from the pan to the cooling rack.
To avoid jam spilling out during rolling, spread only a thin layer of the jam to the dough.