For the cake - Preheat oven to 350° F. Grease an 8-inch square baking pan with butter and line with parchment paper allowing enough paper to come up the sides of the pan and over the top edges forming a “sling.” Beat butter, sugar and lemon zest with a stand mixer fitted with the paddle attachment, or a hand mixer, until light and fluffy. Add eggs, one at a time, scraping down the sides of the bowl after each addition. Whisk together flour, baking powder, salt and ginger together in a small bowl. Alternately add the flour mixture and sour cream starting and ending with the dry ingredients mixing between each addition until just combined.
Transfer the batter to the prepared pan and spread even with a spatula. Place dollops of the Gingerbread Butter over the top, swirl and poke into the batter with a knife (do not mix in completely).
For the crumb topping - Combine the flour, oats, brown sugar, salt and cinnamon in a medium bowl. Add butter and mix with a fork until well combined and crumbs form. Sprinkle the crumb mixture evenly over the top of the cake. Bake for 35-45 minutes. The cake is done when a toothpick inserted in the center of the cakes comes out clean (avoid sticking the toothpick into the chutney or butter). Cool completely.
Remove cake by running a knife along the edges of the cake that touch the pan. Gently remove the cake by lifting the sling. Place on a cutting board. Cut into 2-inch squares and serve immediately. (Can also be stored several days in an air tight container.)