Combine the yeast, bread flour, oat flour, salt, brown sugar and warm water in the bowl of your stand mixer. Using the dough hook attachment on low speed, knead until the dough is smooth, about 7 minutes. Add the dried blueberries and knead for 5 more minutes. The dough should be stiff and smack the sides of the bowl.
Coat a large bowl with about a tablespoon of vegetable oil and add dough. Roll the dough ball around to coat it in oil. Loosely cover with plastic wrap and let the dough sit in a warm place for about 1 hour. The dough should be roughly doubled in size.
Gently deflate the dough and turn it out onto a clean cutting board. Divide the dough into 8 equals portions - I used a chef's knife to cut the dough. Roll each piece of dough into a ball and loosely cover the balls with plastic wrap. Allow the dough balls to rise for 30 minutes.
In a wide, shallow pan, combine the two quarts of water with the sugars. Bring to a boil then reduce to a simmer. Preheat oven to 425 degrees F.
To shape the bagels, poke a hole in the middle of each dough ball. Twirl the dough around the index fingers of your two hands until the hole stretches to about 2 inches. Place the newly formed bagel on a parchment or silpat covered baking sheet. Shape the remaining dough balls.
Drop the bagels, 3 or 4 at a time, into the simmering water. Simmer the bagels for 2 minutes and flip over to simmer for another minute. Remove the bagels from the water bath with a large slotted spoon and let cool for a few minutes on the parchment-lined baking sheet.
Bake the bagels for 20-25 minutes, or until your bagels are golden brown. Remove from the oven and allow to cool on a rack.