Preheat the oven to 350°F. Grease a 9-inch or 10-inch round springform pan or cake pan.
Wash the blackberries in a colander or sieve. Set them aside to air dry while you prepare the cake batter.
In a mixing bowl, whisk 2 cups of the flour with the cinnamon, baking powder, baking soda, and salt. Set aside.
In a separate large mixing bowl with a hand mixer or in the bowl of a stand mixer with the paddle attachment, beat the softened butter and granulated sugar until it is fluffy.
Add the lemon zest, lemon juice, eggs, and vanilla extract. Beat the mixture again to combine everything. (It’s okay if it looks split at this point; everything will come together once the dry ingredients are mixed in.)
Add the milk and mix just until it’s combined.
Add the dry ingredients into the wet ingredients and gently mix with a large spoon or spatula until you no longer see dry pockets of flour. Scrape the sides and bottom of the bowl to ensure everything is well mixed. Set aside.
In a small bowl, toss the blackberries in 1 tablespoon of flour. Add the coated blackberries to the cake batter, leaving any excess flour in the bowl. Gently fold them into the batter.
Spread the cake batter into the greased cake pan in an even layer. Dollop small spoonful’s of the blackberry jam on top, and use a knife to gently swirl the jam into the batter.
Bake for about 35 to 40 minutes, until a toothpick or knife inserted into the center of the cake comes out clean.
While the cake cools, make the glaze. Mix in the powdered sugar, lemon zest, salt, and one tablespoon of lemon juice. Mix in another teaspoon of lemon juice at a time until it’s still thick, but a drizzle-able consistency.
Remove the cake from the cake pan, then drizzle the glaze over the top, allowing it to drip down the sides. Slice & enjoy!