In a 2-cup liquid measure, dissolve yeast and 1 teaspoon sugar in warm water. Let stand until foamy, about 5 minutes.
Cut butter into 1-inch pieces. Insert dough blade in work bowl; add flour, sugar, salt and butter. Process to combine. Add ice water and eggs to yeast mixture. With machine running on dough speed, add liquid mixture through small feed tube in a steady stream only as fast as the flour will absorb it. Dough is very soft and will not form a ball. Continue processing for 45 seconds.
Shaping Rising and Baking
Place dough in a lightly oiled or floured plastic food storage bag. Shape into a flat disk; squeeze air out, allowing space for dough to rise. Refrigerate 6 to 24 hours.
Grease a 3-cup capacity brioche pan. On well-floured surface divide dough into 4 sections.
Divide 1 section into 2 equal parts; set aside 1 part. Using 3 sections plus the remaining part, shape into a smooth ball and place into pan. Press ball to fill pan. Using two fingers, make a hole in the center through to the bottom. Form remaining part into a smooth ball. Shape into a plug by tapering one side; insert in the hole so that it makes a small round, sitting on top the first piece. Cover loosely with plastic wrap coated with vegetable oil cooking spray; let rise until doubled and indentation remains after lightly touching dough, about 30 to 40 minutes. Preheat oven to 400ºF for 15 minutes before baking.
Combine egg yolk and milk. Gently brush glaze on rolls. Bake until golden brown, about 30 to 35 minutes. Remove from pan; place on wire rack. Best served warm; reheat if necessary.
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