Dissolve the yeast and 1/4 cup sugar in warm milk and let stand until foamy, about 5-10 minutes.
In a bowl, combine 3 cups of flour and salt. Add the yeast mixture, eggs, and butter. Knead until smooth and elastic.
Cover the dough and let it rise in a warm place until doubled, about 1 to 1.5 hours.
For the filling, mix cream cheese with 1/4 cup sugar until smooth.
Punch down the dough and roll it out. Spread the cheese filling over it, then roll it into a log.
Place the roll in a greased baking pan and let it rise again for about 30 minutes.
Preheat oven to 350°F (175°C). Bake the babka until golden brown, about 45 minutes.