Make the mint syrup. In a small saucepan, combine sugar and water.
Warm over medium heat, stirring until the sugar dissolves and the mixture gently simmers. Remove from heat, add the mint leaves, and steep for 15–20 minutes. Strain, pressing on leaves to extract flavor.
Stir in bourbon (or vanilla). Let cool.
Prep the pan and oven. Heat oven to 350°F (175°C). Grease and line an 8-inch round or 9-inch square pan with parchment, leaving overhang for easy removal.
Mix dry ingredients. In a large bowl, whisk flour, sugar, baking powder, baking soda, and salt until well combined.
Mix wet ingredients. In a separate bowl, whisk eggs, oil, buttermilk, and vanilla until smooth.
Add lemon zest and chopped mint if using.
Combine. Pour wet ingredients into dry. Stir gently with a spatula until just combined. Avoid overmixing; a few small lumps are fine.
Bake. Transfer batter to the prepared pan and smooth the top.
Bake 22–28 minutes, until the center springs back and a toothpick comes out clean or with a few moist crumbs.
Soak with mint syrup. While warm, poke the cake all over with a skewer or fork. Brush or spoon 1/3 to 1/2 cup mint syrup evenly over the surface, letting it absorb. Reserve the rest for the glaze.
Cool completely. Let the cake cool in the pan 10 minutes, then lift out and cool fully on a rack.
Glaze. Whisk powdered sugar with 2–3 tablespoons mint syrup and a pinch of salt until pourable.
Add a splash of bourbon if desired. Drizzle over the cooled cake and let set for 10–15 minutes.
Serve. Garnish with fresh mint leaves. For a lighter finish, skip the glaze and serve slices with a dollop of softly whipped cream and a drizzle of leftover syrup.