Make the blackberry base first: Blend the blackberries until smooth, then press through a fine mesh sieve to remove seeds. Pour the puree into a small saucepan and simmer over medium-low heat, stirring often, until reduced to about 1/3 cup and thickened, 5–7 minutes. Transfer to a shallow bowl and cool completely.
Heat the oven to 350°F. Line a 12-cup muffin pan with liners and place 2 more liners in a second pan (this batter makes about 14 cupcakes).
Rub the lemon zest into the sugar with your fingertips until the sugar feels slightly damp and very fragrant, about 30 seconds. This releases the citrus oils into the batter.
In a separate bowl, whisk together the flour, baking powder, and salt until evenly combined.
Whisk the oil, eggs, and vanilla into the lemon sugar until lightly foamy, about 1 minute. Whisk in the buttermilk and lemon juice until smooth.
Sprinkle the dry ingredients over the wet and whisk just until a smooth batter forms; do not overmix. Let the batter rest 10 minutes to hydrate for a finer crumb.
Fill liners about 2/3 full. Bake 16–18 minutes, rotating the pan once, until the tops spring back and a tester comes out clean. Cool in the pan 5 minutes, then transfer to a rack to cool completely before frosting.
For the buttercream, bring 1 inch of water to a bare simmer in a saucepan. In the bowl of a stand mixer, whisk together the sugar, honey, egg whites, cream of tartar, and salt. Set the bowl over the pan (without touching the water) and whisk constantly until the mixture reaches 160°F and no sugar grains remain, 3–5 minutes.
Move the bowl to the mixer with the whisk attachment and beat on medium-high until glossy, stiff peaks form and the bowl feels cool, about 8–10 minutes.
Reduce speed to medium and add the softened butter a tablespoon at a time until fully incorporated. Keep mixing until the frosting becomes thick and silky, then mix in the vanilla. Tip: If the buttercream looks curdled, keep beating; if it’s soupy, chill the bowl for 10 minutes and beat again.
Beat in 2–3 tablespoons of the cooled blackberry reduction (add gradually to reach your preferred color and flavor), along with the lemon zest and lemon juice. Switch to the paddle attachment and mix on low for 1 minute to smooth out air bubbles.
Pipe tall swirls of blackberry buttercream onto the cooled cupcakes. Serve at cool room temperature. Optional: top each with a fresh blackberry and a whisper of lemon zest.