Preheat oven to 350°F. Line an 8-inch square pan with lightly greased parchment paper.
Make the cinnamon crumb mixture by combining brown sugar, flour, and cinnamon together in a bowl. Add chilled butter cubes with a pastry cutter or two forks until the mixture is in smaller crumbs.
To make the cake: Whisk the flour, baking powder, baking soda, and salt together in a large bowl. Set aside. In another large bowl using a handheld or stand mixer fitted with a paddle attachment, beat the butter and sugar together on high speed until creamy, about 2 minutes. Scrape down the sides and up the bottom of the bowl as needed.
Add the eggs and vanilla, and mix on medium speed until just combined. Beat in the Greek yogurt, scraping down the sides of the bowl with a spatula.
Add the flour mixture to the wet ingredients, and beat on low speed until just combined. Finally, beat in the milk.
Spread half of the batter into the 8x8" pan. Sprinkle half of the crumb mixture on top of the cake batter. Use a spoon or offset spatula to carefully add the rest of the cake batter on top of the crumb mixture. You'll have to go slowly here. Sprinkle the rest of the crumb mixture evenly on top.
Bake cake for around 32 minutes or until a toothpick inserted into the center of the cake comes out clean. Let the cake cool in the pan 10 minutes before removing to a cooling rack.
Notes
Storage: Store coffee cake at room temperature in an airtight container for 3-4 days. You can also store in the refrigerator to make it last for a couple more days. To freeze: This coffee cake can be frozen. Frozen individual pieces tightly in plastic wrap. Take out a piece at a time to bring to room temperature in the refrigerator.