1. Dissolve yeast in warm milk in the bowl of a stand mixer fitted with the paddle attachment; let stand 5 minutes. Weigh or lightly spoon flour into dry measuring cups; level with a knife. Add flour, sugar, salt, and eggs to milk mixture; beat with a stand mixer at low speed until smooth, scraping down sides of bowl with spatula as needed. Remove paddle attachment; insert dough hook. Beat dough at low speed 5 minutes or until soft and elastic and dough just begins to pull away from sides of bowl. Cut 6 1/2 tablespoons butter into large cubes; add half of butter to dough, mixing at medium speed to blend. Add remaining butter cubes to dough; beat at medium speed until incorporated. Beat dough at medium speed 4 minutes or until smooth and elastic.
2. Place dough in a large bowl coated with cooking spray, turning to coat top. Cover and let rise in a warm place (85°), free from drafts, 1 hour or until doubled in size. (Gently press two fingers into dough. If indentation remains, dough has risen enough.) Punch dough down; form into a ball. Return dough to bowl; cover with plastic wrap, and refrigerate 8 hours or overnight.
3. Uncover dough; let stand 90 minutes or until dough is at room temperature. Divide dough into 4 equal portions. Working with one portion at a time (cover remaining dough to prevent drying), cut dough into 6 equal pieces. Roll each piece into a 1 1/2-inch ball. Repeat procedure with remaining 3 dough portions to make 24 rolls total. Place rolls in muffin cups coated with cooking spray. Cover and let rise for 45 minutes or until almost doubled in size.
3. Preheat oven to 350°.
4. Combine 1 tablespoon water and egg white; stir with a whisk. Gently brush rolls with egg mixture. Bake at 350° for 14 minutes or until golden. Place pans on wire racks. Place remaining butter in a microwave-safe bowl; microwave at HIGH 20 seconds or until butter melts. Brush butter onto rolls.