Sprinkle yeast and 1 teaspoon sugar over milk in small, shallow bowl. Cover with plastic wrap and place in warm place until yeast blooms and mixture nearly doubles in volume, 5 to 10 minutes.
Combine flour, 1 tablespoon sugar and salt in large mixing bowl. Make well in flour mixture and add milk-yeast mixture and softened butter. Beat vigorously with large spoon until smooth. Form into ball and place on lightly floured surface. Knead hard 10 minutes, adding more flour or water as needed to create medium stiff dough.
When dough is smooth and elastic, place in large, lightly buttered bowl. Cover with plastic wrap and kitchen towel and let rise in warm, draft-free place, such as unlit oven with pilot light on, until doubled in bulk and dough springs back slowly when gently poked with finger, 45 minutes to 1 hour. Punch dough down and let rise until again doubled, 30 to 40 minutes.
Punch dough down and roll out on lightly floured surface into circle about 22 inches in diameter. If rolling surface is too small, divide dough in half and roll into 2 half-circles 22x11 inches.
Roll dough up on rolling pin and unroll carefully over buttered 9-inch cake or springform pan or springform so that it is centered, with edges overlapping more or less evenly on all sides. If using 2 half-circles of dough, form 1-inch seam to make whole circle and moisten thoroughly to seal. Carefully press center of dough down to bottom of pan.
For cheese filling, combine cheese, butter and egg in large mixing bowl. Knead vigorously until texture is uniform. Shape into a thick, round cake-like form that is 8 to 7 1/2 inches in diameter. Place Cheese Filling on dough and bring up edges of dough over filling, forming thick, fabric-like folds. Moisten edges at top and seal.
Let stand 10 to 15 minutes. Bake at 375 degrees in center of oven, with foil underneath in case filling leaks, until golden brown, 50 minutes to 1 hour. Cool 1 to 2 hours before serving.