Preheat the oven to 425°F (220°C). Grease a 12-cup muffin tin and line with muffin liners.
In a medium bowl, whisk together the flour, baking powder, and salt.
In the bowl of a stand mixer, massage the sugar and lemon zest together until fragrant and pale yellow.
Add the butter to the bowl of lemon sugar and fit the stand mixer with a paddle attachment. Beat on medium speed for 1-2 minutes until pale and fluffy.
Scrape down the bowl then add the eggs one at a time, mixing well in between each addition. Scrape down the bowl again and add the sour cream, milk, vanilla extract, and almond extract. Mix until well combined. Scrape down the bowl once more.
Add the flour mixture and mix on low speed until there's a few streaks left. Remove the bowl from the stand mixer and fold in the halved blackberries until just combined. Be careful not to break up the berries too much or overmix the batter.
Use a large cookie scoop to evenly transfer the batter to the prepared muffin cups. Generously sprinkle the tops with coarse sugar.
Bake for 10 minutes then reduce the temperature to 350°F (180°C) and continue baking for 8-10 minutes or until a cake tester inserted into the center comes out clean or ideally with a few soft crumbs. DO NOT open the oven door when reducing the temperature.
Let the muffins cool in the pan for 5-10 minutes then use a fork to gently lift them out and transfer to a wire rack. Cool completely or until lightly warm. Enjoy!