Preheat oven to 350 degrees F. Grease or line a 9x9 pie pan or 8x8 square baking pan with parchment paper.
To make the curd, place the blackberries into a blender and blend until smooth. Strain the seed through a fine mesh strainer, and place the blackberry purée into a medium saucepan. Discard seeds.
Heat the saucepan with the blackberries over medium heat. Add the lemon juice and sugar. Whisk until the sugar has dissolved, for about 3-4 minutes.
To temper the eggs, place the egg yolks in a small bowl. Take about 1/4 cup of the hot blackberry purée and slowly pour it into the eggs, whisking continuously. Once all the blackberry purée has been added, pour the eggs into the saucepan with the blackberries, whisking as you do it.
Place 1 tablespoon of butter at time into the blackberry curd, whisking until each tablespoon has fully melted before adding the next tablespoon. Continue to do this until all the butter has been added. At this time, the curd should be able to coat the back of a spoon. If not, continue to cook over medium heat, whisking, while it does.. Turn off heat and let cool. The curd will continue to thicken as it cools.
To make the coffee cake batter, mix the flour, baking powder, baking soda, and salt together in a bowl. Whisk until combined and set aside.
In a separate large bowl, Add in the eggs, greek yogurt, maple syrup, oil, buttermilk, vanilla extract. Using an electric mixer or whisk, mix until fully combined.
Pour the flour mixture into the wet ingredients and stir until just mixed. It is ok if there are still some lumps.
To make the crumb topping, combine the brown sugar, flour, cinnamon, and salt together. Add in the cold cubed butter. Using a pastry cutter (or fork), cut the butter into the cinnamon sugar mixture. Continue to mix until it resembles sand like texture.
Pour the batter into the greased or lined baking dish. Top with 3/4 of the blackberry curd (or all of it if you do not wish to reserve any for drizzle after baking). Sprinkle the crumb topping evenly over the blackberry curd.
Bake for 28-35 minutes or until the coffee cake batter is set. There still may be a jiggle from the blackberry curd, but a toothpick should not have any batter on it.
Let cool. Drizzle reserved blackberry curd over each slice if desired and enjoy!