Heat the oven to 400 degrees F. with a rack in the center.
Oil the bottoms of three cavities of a muffin tin. Brush the top of the muffin tin with oil around the three cavities that you will be using.
In a medium bowl, whisk together the flour, oats, brown sugar, baking powder, and salt. Add the dried blueberries and stir.
In a small bowl, whisk the applesauce, oil, egg yolk, and vanilla.
Pour the liquid ingredients into the dry ingredients and stir until the ingredients are just combined.
Divide the batter among the three prepared muffin cavities.
Top each with the streusel mixture. Press it lightly into the batter.
Fill the rest of the cavities of the muffin tin halfway up with water.
Bake the muffins or 18 to 20 minutes, until a toothpick comes out clean.
Let the muffins cool in the pan for 5 minutes.
Remove the muffins from the pan and cool on a wire rack for another five minutes before serving.