Place warm water in the bowl of a stand mixer fitted with a dough hook OR a large bowl. Dissolve yeast in water and let stand 5 minutes until foamy.
Mix sugar and egg into yeast mixture until smooth. Add salt and 3 cups flour to bowl and mix on low speed OR with a wooden spoon if making dough by hand until dough pulls away from sides of bowl, about 2 minutes of mixing (if dough seems a bit wet, add additional flour by the tablespoon until dough pulls away from sides of bowl)
Add softened butter by the tablespoon while mixer is running or fold in by hand with a wooden spoon until butter is combined in the dough.
If making dough in stand mixer, knead dough in mixer on low speed 5-7 minutes until dough is stretchy and elastic. If making dough by hand, turn dough onto a lightly floured surface and knead by hand until dough is stretchy and elastic, about 10 minutes of kneading.
Place dough in a greased bowl, turning once to grease top. Cover bowl with plastic wrap and let rise in a warm place at room temperature 1 to 1-1/2 hours until dough is doubled in size.
Lightly grease a 9-inch square baking dish. Punch risen dough down and divide into 12 equal pieces. Roll each portion into smooth balls and arrange in baking dish. Cover pan with plastic wrap and refrigerate rolls 8 hours or up to 16.*
When ready to bake rolls, remove pan from refrigerator and allow rolls to rise at room temperature 30-45 minutes until rolls are slightly puffy. Brush rolls with egg white wash.
Preheat oven to 350F. Bake dinner rolls at 350F 25-30 minutes until rolls are a deep golden brown and register 190F on a kitchen thermometer. Cool rolls on a wire cooling rack.
Serve rolls warm or reheated with butter if desired. Enjoy!