First, dice about 2 cups of fresh strawberries into small pieces. In a mixing bowl, combine the strawberries with lemon zest, lemon juice and brown sugar. Stir the mixture occasionally and mash the solids with the back of a spoon or potato masher to extract the juices from the berries. Set aside.
Next, add water to the bowl of a stand electric mixer. Sprinkle the yeast and a pinch of brown sugar over the water's surface and stir to combine. Let it sit for 10 minutes until bubbles appear, indicating the yeast is activated.
Once activated, add the macerated berries, one cup of flour and salt to the yeast mixture. Use the paddle attachment or a wooden spoon to blend everything together well. Then gradually mix in the remaining flour until a thick, tacky dough forms that cleans the sides of the bowl. Change to the dough hook and knead for about 5 minutes.
Grease a large mixing bowl with oil. Transfer the kneaded dough to the bowl and coat it evenly with additional oil. Cover with plastic wrap and let rise for 1 to 1.5 hours until doubled in size.
Once risen, turn the dough out onto a floured work surface and divide into 12 equal portions. Shape each portion into a smooth, tight ball, pinching the bottom seams. Place the balls on a tray covered with plastic wrap and let rest for 20-30 minutes.
While resting, heat water and sugars in a large pot to a gentle boil. Grease two baking sheets with parchment paper and preheat oven to 425°F.
Working with one ball at a time, poke a hole through the center and stretch into a 1-inch diameter ring. Cook batches of 4 bagels each for 2 minutes per side in the simmering water. Bake for 20-25 minutes until golden brown. Cool completely before serving.