In the bowl of a stand mixer, combine 2 cups flour, 2 tablespoons sugar, salt, and yeast; mix well using the paddle attachment.
2 ½ to 3 cups all-purpose flour, 2 tablespoons sugar, 1 teaspoon salt, 2 ¼ teaspoons quick rise yeast
In a small saucepan or microwave-safe dish, combine ¾ cup milk, water, and butter. Heat to 120° to 130º.
¾ cup milk, ¼ cup water, 3 tablespoons butter
Add warm liquid to flour mixture; blend at low speed until moistened. Beat 3 minutes at medium speed.
Switch to the dough hook and mix in the remaining flour a little at a time to make a soft dough, adding more or less flour as needed. Knead the dough for 5 minutes. Place in a greased bowl, turning to grease top. Cover; let rise in a warm place (80° to 85º) until light and doubled in size, 45 to 60 minutes.
2 ½ to 3 cups all-purpose flour
Grease a 12-inch pizza pan or baking sheet.
In a shallow dish or pie pan, combine nuts (if using), ½ cup sugar, brown sugar, and cinnamon; mix well. Place melted butter in another shallow dish or pie pan.
½ cup sugar, 2 tablespoons brown sugar, 1 teaspoon cinnamon, ½ cup butter
Punch down dough. Turn dough out onto a lightly floured surface. Divide dough into 12 equal pieces and keep pieces covered with plastic wrap.
On a lightly floured surface, roll each piece of dough into a 12-inch long rope. Dip each dough rope in butter and then roll in sugar mixture to coat evenly.
½ cup butter
Place 1 strip in the center of the pan, winding to form a coil. Repeat with remaining dough, placing close together to make a round, flat coffee cake.
Cover; let rise in warm place until doubled in size, 45 to 60 minutes.
Preheat oven to 350º. Uncover coffee cake. Bake 20 to 25 minutes or until golden brown.
Cool 5 minutes on baking sheet. Carefully remove from pan; place on serving plate.
In small bowl, combine glaze ingredients, adding enough milk for desired drizzling consistency. Drizzle over warm coffee cake and serve.
1 to 2 teaspoons milk, ½ cup powdered sugar