Combine 2 cups flour, sugar, dry yeast and salt in a large mixer bowl and stir until blended. Place water and butter in a microwave-safe bowl. Microwave on HIGH in 15 second increments until very warm but not hot to the touch (120° to 130°F. Butter won’t melt completely). Add to flour mixture with egg.
Beat 2 minutes at medium speed of electric mixer, scraping bowl occasionally. Add 1 cup flour; beat 2 minutes at high speed, scraping bowl as needed. Stir in just enough remaining flour so that the dough will form into a ball.
Knead on lightly floured surface until smooth and elastic, and dough springs back when lightly pressed with 2 fingers, about 6 to 8 minutes. Cover with a towel; let rest for 10 minutes.
For filling, combine sugar and cinnamon in a small bowl. Set aside.
Divide dough in half. Roll 1 half into a 12 x 10-inch rectangle on a lightly floured surface using a rolling pin. Spread 1-1/2 tablespoons butter over dough leaving a 1-inch border on the long edges. Sprinkle with half of the cinnamon sugar mixture. Beginning at long end of rectangle, roll up tightly. Pinch seams to seal. Cut into 12 equal slices. Place 8 rolls, cut sides down, on greased baking sheet. Leave plenty of room around each roll. Gently unroll remaining 4 rolls, resulting in 4 long strips. Cut each into 4 equal pieces. Position 2 strips as "ears" for each roll, tucking an edge under roll. Turn down top edge to make a "floppy ear." Repeat with second half of dough. Cover with towel; let rise in warm place until doubled in size, about 30 minutes.
Bake in preheated 350ºF oven for 15 to 20 minutes or until rolls are golden brown. Cool on pan for 5 minutes, then carefully remove to wire rack to cool an additional 15 minutes.
Combine all frosting ingredients (start with 3 tablespoons milk and add more if needed) in a large bowl and beat until creamy. Remove 1/4 cup icing and place in a small bowl; set aside Spread remaining icing over rolls. Add a drop of red food coloring to reserved icing to create a light pink color. Frost pink icing over the ears. Decorate faces with small candies for eyes and nose, add licorice whiskers and use sliced almonds for teeth.