For the dough: In the bowl of a mixer with the dough hook, combine the levain, flour, soft butter, granulated sugar, whole eggs, egg yolk, milk and salt. Knead on low speed for 25 to 30 minutes, stopping the mixer and scraping it down every 10 minutes or so to make sure everything is getting incorporated, until the dough comes together in a smooth ball and pulls away from the sides of the bowl.

Transfer the dough to a large bowl coated very lightly with neutral nonstick cooking spray. Cover and set in a warm spot, letting the dough proof for 4 hours at room temperature.

Gently fold the dough over itself, cover and transfer to the fridge to ferment overnight, 12 to 14 hours.

For the filling: Combine the cream cheese, powdered sugar, egg yolk, lemon zest and salt in a mixing bowl. Cream together until smooth.

When the dough has fermented for about 12 hours, spray a 9 x 4 x 4-inch loaf pan with neutral nonstick cooking spray.

Remove the dough from the fridge and gently turn it out onto a floured work surface. Dust the top of the dough lightly with flour and gently roll it out into a 10 x 20-inch rectangle.

Spread all the filling over the dough in an even layer. Then dust evenly with the poppy seeds.

Roll the dough up starting with the short edge to form a 10-inch long spiral. Cut the roll down the middle the long way, creating two strips.

Place the middle of one half on top of the middle of the other half—forming an X—then twist the strips around one another.

Place the twisted dough in the pan, tucking in the ends. Spray the top of the babka lightly with a nonstick spray and cover loosely with plastic.

Place the babka in a warm spot and proof again, until it increases in size by about a third and is light and puffy in appearance, 3 to 4 hours.

Heat the oven to 350F degrees with a rack in the center. When fully proofed, transfer the babka to the oven and bake until a deep golden brown on top, 45 to 55 minutes.

For the glaze: While the babka bakes, bring the water, sugar and lemon zest to a boil in a small pot. Boil for 2 minutes to reduce slightly, stirring occasionally.

Remove from the heat. Remove the babka from the oven and immediately pour the glaze over the top, using it all.

When cooled to room temperature, gently unmold, slice and enjoy.