Combine milk, 3/4 cup water, and honey in a small saucepan. Heat milk mixture over medium-high heat to 100° to 110°; remove from heat. Dissolve yeast in milk mixture; let stand 5 minutes. Stir in butter and egg.
Lightly spoon flour into dry measuring cups; level with a knife. Combine 4 cups flour, oats, and salt in a large bowl, stirring well. Add yeast mixture to flour mixture; stir until a soft dough forms. Turn dough out onto a lightly floured surface. Knead until smooth and elastic (about 8 minutes); add enough remaining flour, 1 tablespoon at a time, to prevent dough from sticking to hands.
Place dough in a large bowl coated with cooking spray, and turn to coat top. Cover and let rise in a warm place (85°), free from drafts, 1 hour or until doubled in size.
Punch dough down, reshape into a ball, and return to bowl. Cover and let rise 1 hour or until doubled in size.
Punch dough down; turn out onto a lightly floured surface. Knead dough 3 to 4 times; let rest 5 minutes. Divide mixture into 24 equal portions; shape each portion into a ball. Place balls 1 inch apart on a jelly-roll pan coated with cooking spray. Cover and let rise in a warm place (85°), free from drafts, 30 minutes or until doubled in size.
Preheat oven to 425°.
Bake rolls at 425° for 12 minutes or until browned. Remove rolls from pan; cool on a wire rack.