Prepare the ingredients. In a large bowl, measure out the flour, sugar, salt, and yeast. Mix thoroughly.
Dice the pineapple into small cubes and set aside. It's important that it's not too moist, so pat off any excess moisture with a paper towel.
Add the warm water to the dry ingredients and start kneading the dough. Once it begins to come together, add the melted butter and pineapple pieces. Continue kneading for about 10 minutes, until 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.
Punch down the risen dough and divide it into 8 equal portions. Shape them into balls, then use your finger to make a hole in the center and shape them into bagels.
Let the shaped bagels rest for another 15 minutes. Meanwhile, heat a large pot of water and add a little honey.
Drop the bagels into the hot water one at a time and cook them for about 30 seconds per side. This helps them get a shiny and crispy crust on the outside.
Preheat the oven to 400°F (200°C). Place the cooked bagels on a baking sheet lined with parchment paper and optionally sprinkle with a little honey for extra sweetness.
Bake the bagels for about 20 minutes, or until golden brown and crispy.
Let them cool, then serve fresh, perhaps with a few extra pineapple chunks or cream cheese!
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