Preparation

1. Heat 1 cup of water in a small pot over high heat until it starts to bubble. Measure the temperature with an instant-read thermometer, adding cool water until the temperature drops to 130 degrees F. Pour 1 cup of the water into a measuring cup and add the vegetable oil and vinegar.
2. In a large bowl, mix the whole wheat flour, all-purpose flour, sugar, yeast and salt. Stir in the warm water mixture until it becomes a shaggy mass (lumpy yet well-mixed), then switch to kneading with your hands. Knead until it forms a soft dough.
3. Oil a large mixing bowl and scrape the dough into the bowl. Cover tightly with plastic wrap and let rise in a warm place for at least 45 minutes or until dough has doubled in size.
4. Line two sheet pans with parchment paper. Preheat the oven to 375°F. Divide the dough into 8 even portions.
5. To form bagels, roll each portion under your palm on the counter to make a 6-inch long rope. Coil the rope around two of your fingers and press the ends together to seal, then roll between your fingers to make a smooth circle where the joint is sealed. Place each on the prepared sheet pan, leaving 2 inches between the bagels. Cover lightly with a damp kitchen towel and let rise in a warm spot for at least 30 minutes or until the dough has again doubled in size.
6. Just before baking, whisk the egg with 1 teaspoon of water and brush the bagels with egg, then sprinkle the bagels with any desired toppings. Bake for 15 minutes at 375°F. Slide the bagels off the pan onto a rack to cool.