Preheat oven to 350°F (177°C). Grease and flour a 9x13 baking pan or line with parchment.
Make streusel: mix brown sugar, cinnamon, and salt. Stir in melted butter, then flour until crumbly. Set aside.
Make cinnamon filling: combine softened butter, flour, brown sugar, and cinnamon until soft crumbs form. Set aside.
Make cheesecake filling: beat cream cheese until smooth. Add sugar, then eggs, then vanilla. Mix until creamy. Set aside.
Make cake batter: whisk flour, granulated sugar, baking soda, baking powder, and salt. Beat in softened butter until evenly crumbly. Add eggs, vanilla, and milk. Mix until smooth without overmixing. Spread into prepared pan.
Assemble: spread the cinnamon filling evenly over the batter. Spoon and spread the cheesecake filling over the cinnamon layer. Top evenly with streusel.
Bake 60–75 minutes, checking the center with a toothpick. It should come out clean or with moist crumbs.
Cool completely in the pan, then refrigerate 3–4 hours so the cheesecake layer sets.
Glaze: whisk powdered sugar, milk, and vanilla until smooth. Adjust thickness as needed. Drizzle over the chilled cake. Slice and serve.