In the bowl of a stand mixer, using the paddle attachment, combine 2 cups flour, 2 tablespoons sugar, salt, and yeast; mix well.
In a small saucepan or microwave safe dish, combine ¾ cup milk, water, and butter. Heat to 120 to 130º.
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.
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.
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 to coat; roll in sugar mixture to coat evenly.
Place 1 strip in the center of the pan; wind 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.
Glaze: In small bowl, combine glaze ingredients, adding enough milk for desired drizzling consistency. Drizzle over warm coffee cake.
Notes
*If desired, add ¾ cup finely chopped nuts to the Cinnamon Sugar Coating.