Prepare the streusel by combining the flour, brown sugar, cinnamon, and melted butter in a mixing bowl. Use a fork to mix the mixture until it's crumbly, like clumpy wet sand. Set aside.
Preheat the oven to 350°F. Line a baking sheet with parchment paper.
In a large mixing bowl, whisk together the flour, baking soda, salt, cinnamon, and nutmeg. Set aside.
In a separate large mixing bowl, beat the softened butter with the brown sugar with a stand mixer or a hand mixer until it is creamy and well combined.
Use a couple paper towels to blot excess liquid off your applesauce, then add that along with the eggs and vanilla extract to the butter mixture. Beat it until everything is fully mixed in.
Add the dry ingredients to the wet ingredients. Mix the dough with a large spoon or spatula just until there is no visible dry flour.
Use a large cookie scoop or two spoons to drop cookie dough balls (about 2 inches in diameter) onto the baking sheet, spread out at least 2 inches apart. Gently flatten each cookie ball slightly with the back of your cookie scoop or spoon.
Sprinkle the streusel on top of each cookie, gently pressing it into the dough to get it to stick on the top and sides.
Bake for 12 to 14 minutes, just until the cookies are golden around the edges and don’t feel super squishy on top. Allow them to cool and firm up for a few minutes, then enjoy!!