Preheat oven to 350° Fahrenheit. Line 9x13 baking dish with parchment paper.
In small bowl, mix together brown sugar, all-purpose flour, and cinnamon to create cinnamon-sugar filling. Set aside.
In separate small bowl, use hand mixer to mix together butter, light brown sugar, and all-purpose flour to create streusel topping. Set aside.
In large bowl, whisk together wet ingredients for coffee cake: applesauce, vanilla extract, coconut oil, non-dairy milk, and apple cider vinegar. Let mixture sit 5 minutes.
In separate large bowl, whisk together dry ingredients for coffee cake: all-purpose flour, granulated sugar, baking powder, and salt. Set aside.
When 5 minutes is up, slowly pour wet ingredients for coffee cake into large bowl with dry ingredients for coffee cake. Mix until ingredients are just combined.
Pour half of coffee cake mixture into lined baking dish. Add cinnamon-sugar filling to top of cake mixture, distributing evenly edge to edge.
Pour remaining coffee cake mixture on top of cinnamon-sugar filling layer. Crumble streusel topping over top of cake batter.
Place baking dish in preheated oven and bake 30-35 minutes. Toothpick inserted in center of cake should come out clean or with very few crumbs.
Remove baked coffee cake from oven and let cool completely in baking dish. While cake cools, whisk together all ingredients for glaze, if desired.
When cake is cool, drizzle glaze over top of cake. Cut coffee cake into squares and serve.