In a large bowl, combine the flour, yeast, sugar, and salt. Make sure the salt doesn't come into direct contact with the yeast, as it can inhibit its activity.
Add the warm water and rum, then mix with a wooden spoon until the dough comes together. Once it's manageable, start kneading by hand for about 10 minutes, until it becomes smooth and elastic.
Cover the dough with a kitchen towel and let it rise in a warm place for about 1 hour, or until doubled in size.
Finely chop the candied orange peel, then knead it into the risen dough until evenly distributed.
Divide the dough into 8 equal portions and shape them into balls. Use your finger to make a hole in the center of each ball, and gently stretch it out to form a bagel shape.
Bring a large pot of water to a boil, then reduce the heat to a simmer. Boil the bagels one at a time for 30 seconds on each side, then place them on a baking sheet lined with parchment paper.
Whisk the egg with the milk, and brush the tops of the bagels with the mixture. This will help them bake to a beautiful golden brown.
Bake in a preheated oven at 400°F (200°C) for 20-25 minutes, or until golden brown.
Let them cool, then serve fresh, drizzled with a little extra candied orange peel and honey.
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