Preheat the oven to 425 degrees F. Line 12 muffin tins with muffin liners.
In a medium mixing bowl, combine the flour, rolled oats, salt, cinnamon, allspice, baking powder, and baking soda. Whisk together and set aside.
In a large mixing bowl, beat together the eggs and sugar. Add the oil, applesauce, Greek yogurt, milk, and vanilla extract. Mix until combined. Stir in the grated apples.
Pour the dry ingredients into the wet ingredients and stir until just combined. Do not overmix. Let the batter rest for 10 minutes.
While the batter rests, make the oat streusel. Combine the brown sugar, flour, rolled oats, and cinnamon in a bowl. Add the cold butter and cut into the mixture with a pasty cutter or fork until the mixture comes together.
Divide the batter evenly between the 12 muffin tins. Sprinkle the oat streusel generously over each muffin.
Bake at 425 degrees for 5 minutes. Then reduce the heat to 350 degrees F and bake for an additional 13-16 minutes, or until the muffins are fully set and a toothpick comes out clean.
Remove from the oven, let cool, and enjoy!