Beat egg and egg yolk. Add lukewarm water and oil to egg. Beat again, then add to bread machine.
Add flour, then add sugar along one side of the bread pan and salt along the opposite side. Dig a hole in the middle of the flour and add yeast. * NOTE: This is how the ingredients are added in my bread machine (it's old), but follow your bread machine's directions for order of ingredients, if specified.
Turn the bread machine setting to "Dough Mode" and press start.
When dough cycle is complete, remove dough to a lightly floured surface and divide into 2 portions, one slightly larger than the other. *NOTE: You may have to knead in a little more flour than I use, as I live in a very dry climate.
Spray an angel food cake pan with non-stick cooking spray.
Divide the larger piece into two equal pieces, and divide the smaller piece into equal thirds and set aside the smaller pieces (make sure they are covered so they don't dry out).
Shape each of the larger two pieces into a rope about 25 to 30 inches long. (I did mine about 28 inches/71 cm)
Take the two thick ropes, pinch at one end and cross them in an X shape and twist them together until you reach the end, as you would making a cinnamon twist. Then pinch the other end together.
Wrap around inside of the bottom of the prepared angel food cake pan in circular motion.
Take the three smaller ropes and lay them parallel to each other on floured board.
Starting at one end, pinch together, then braid them together as shown.
Arrange the braided rope in a ring on top of the circle of twisted dough, matching the seams up, and pinching the ends to seal.
Preheat oven to 375 degrees (175 degrees C)
Cover (with tea towel) and place in draft-free warm place, to let dough rise for 1 hour or until double in size. *I set the bread to rise on the stove top
Glaze with beaten egg diluted with 1 teaspoon (5 ml) water or milk. * You will only need ¼ - ⅓ of this, not all of it.
Bake at 375 degrees (175 degrees C) for 35-40 minutes until lightly and evenly browned in color.
*Check halfway through the baking process and if it's browned enough on top, (as shown)
If browned enough, then cover with foil and return to oven for remainder of time.
Rest in pan for 5 to 10 minutes. Remove gently and cool.
If you want to make the traditional stacked loaves, then you'll need to make 2 more loaves