In a large bowl, combine the flour, yeast, sugar, and salt. Make sure the salt doesn't directly contact the yeast, as it can inhibit its activity.
Pour in the warm water and vanilla extract, then mix with a wooden spoon until the dough comes together. Once it's manageable, start kneading by hand 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.
Once the dough has risen, chop the strawberries into small pieces, then gently fold them into the dough. Be careful not to overwork the dough, so the strawberries don't make it soggy.
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, then gently stretch it 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 mixture on top of the bagels. 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 slightly, then serve fresh, drizzled with a little honey and garnished with extra strawberry pieces.
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