In a large Dutch Oven pot ( I used my Le Creuset 9qt round) bring 2 ½ quarts water to a boil and cook potato (with skin on) until tender, about 20 minutes or until fork tender.
Remove potato with slotted spoon, reserving all water. When potato is cool, remove skin and mash in a bowl until smooth adding a few drops of cooking water if you need to.
Add honey and olive oil to the mashed potato and stir until creamy.
Combine flour, salt and yeast in the bowl of a stand mixer and with paddle attachment, mix on low. Add potato mixture to flour and 1 cup of reserved cooking water. Mix on medium speed for 10 minutes until dough becomes stiff, yet workable (not sticky).
Turn dough ball out onto counter dusted with flour and knead by hand until smooth and bounces back to the touch- about 5 minutes.
Drizzle a small bit of olive oil in large bowl. Add dough and turn over to make sure it is coated with oil. Cover bowl with a damp dishcloth and place in a warm spot. Let rise until doubled- about 1-2 hours.
Punch dough down in middle, then remove to the counter. Roll into log and cut into 12 equal pieces. Shape each piece into a ball and place on tray lined with parchment paper. Cover again with damp towel and let rise 30 minutes.
Make a hole in center of dough ball with your thumbs and gently work ring around, stretching center about 2 inches. Return to baking sheet and cover again with damp towel and let rest 20 minutes.
Preheat oven to 450.
Bring the cooking water you have set aside back up to a boil. Carefully drop bagels a few at a time into the water. Cook 30 seconds, flip and cook another 30 seconds.
Remove with slotted spoon and place on wire rack to drain. Return bagels to parchment lined baking tray.
Bake bagels for 10 minutes. Beat egg with 1 Tbsp. water; brush egg wash on top of bagels. Immediately sprinkle with everything spice mix. Return to oven and bake 10-12 minutes longer or until deep golden brown.