Preheat oven to 350°F. Lightly grease a 9 x 13 inch pan with butter and line with parchment paper. To make the cinnamon sugar crumble, in a small mixing bowl, combine brown sugar, sugar, flour, cinnamon, and butter. Set aside for later. In a medium size mixing bowl, combine flour, baking powder, baking soda, cinnamon, and salt. Set aside for later. In a stand mixer bowl, cream butter, brown sugar, and sugar together until combined. Add eggs, one at a time. Then add Greek yogurt and vanilla, mix until combined. Gradually mix in the flour mixture until just combined. Then beat in the milk. Next, add golden raisins and grated carrots. Pour 1/2 the batter in the prepared pan. Add spoonfuls of cream cheese on top of the batter. Sprinkle half of the cinnamon streusel over the cream cheese. Pour the rest of the batter over the top. Top with the remaining cinnamon streusel. Bake for 40-45 minutes or until the cake is cooked through. Allow the carrot cake coffee cake to cool for 15 minutes before serving.