Preheat the oven to 350 degrees F. Grease and flour a 10-inch tube pan. Set aside.
Cream the butter and sugar in the bowl of an electric mixer fitted with the paddle attachment for 4 to 5 minutes, until light and fluffy. Add the eggs 1 at a time, then add the vanilla and Greek yogurt. In a separate bowl, sift together the flour, baking powder, baking soda, and salt. With the mixer on low, add the flour mixture to the batter until just combined. Finish stirring with a spatula to be sure the batter is completely mixed.
For the streusel, place the brown sugar, flour, cinnamon, salt, and butter in a bowl and pinch together with your fingers until it forms a crumble.
Spoon half the batter into the pan and spread it out with a knife. Sprinkle with half of the streusel. Spoon the rest of the batter in the pan, spread it out, and scatter the remaining streusel on top. Bake for 50 to 60 minutes, until a cake tester comes out clean.
Let cool on a wire rack. Carefully transfer the cake, streusel side up, onto a serving plate. To make the cream cheese glaze, beat cream cheese and butter together until smooth. Slowly beat in the powdered sugar. Add the vanilla extract and milk. Beat until smooth and until you have a glaze consistency. Drizzle cream cheese glaze over cooled cake and serve.