Preheat oven to 350F (325F convection bake). Butter all sides of a 9" springform pan (or square 9"x 9" baking pan - cook time will vary). Line bottom of pan with parchment paper round/square. Set aside.
In a small/medium bowl, combine the ingredients for your lemon shortbread crumble (flour, butter, sugar, salt, lemon zest) with your clean hands until a mixture resembling wet sand forms. Set aside.
In a large bowl with an electric mixer, cream together butter, oil, and sugar until light and fluffy (approx. 1-3 min). Add eggs, one at a time, followed by vanilla paste/vanilla extract, and yogurt. Mix until well combined. This is your wet mixture.
In a medium bowl, whisk together flour, baking powder, baking soda, and salt. Add dry mixture to the large bowl containing wet mixture. Stir gently until all flour is well incorporated into coffee cake batter. Stop mixing. This is your coffee cake batter.
To your 9" springform pan, add 1/2 of your coffee cake batter. Top with all of your washed, fresh blackberries. Add the remaining half of your coffee cake batter. Top the coffee cake with all of your lemon shortbread crumble.
Bake in oven set to 350F (325F convection bake) for ~70-80 minutes or until a toothpick inserted into the centre comes out clean. Let cool for 10 minutes in springform pan, then remove pan and place onto wire rack.
Dust your coffee cake with powdered sugar.
Cut, serve, and enjoy!