Preheat your oven to 350°F (175°C). Grease a 9x13-inch baking pan and line it with parchment paper for easy removal.
In a medium saucepan, melt the butter over low heat. Once melted, remove from heat and stir in the sugar until well combined.
Add the eggs one at a time, mixing well after each addition, then stir in the vanilla extract.
In a separate bowl, sift together the flour, cocoa powder, baking powder, and salt. Gradually add this dry mixture into the wet ingredients, stirring until just combined. Be careful not to overmix.
In a small bowl, mash the raspberries, honey, and lemon juice together with a fork until you have a slightly chunky raspberry puree.
Pour half of the brownie batter into the prepared baking pan and spread it evenly. Then dollop spoonfuls of the raspberry mixture over the batter.
Pour the remaining brownie batter over the raspberry layer, followed by another swirl of the remaining raspberry sauce on top. Use a knife to gently swirl everything together for a marbled effect.
Bake in the preheated oven for 25-30 minutes or until a toothpick inserted into the center comes out with a few moist crumbs (not wet batter). Let the brownies cool completely in the pan before lifting them out using the parchment paper.
Once cooled, cut into squares and dust with powdered sugar if desired.