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Preheat the oven to 350°F. Thoroughly grease a 10- to 12-cup Bundt pan.
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To make the cake: Prepare your berries by washing and drying them, then roughly chop the blueberries and halve or quarter the blackberries, depending on their size. Leave the raspberries intact (they’ll break down on their own). Set aside.
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Weigh your flour into a medium bowl, or measure it by gently spooning it into a cup, then sweeping off any excess. Whisk the baking powder into the flour.
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In a small bowl or liquid measuring cup, whisk together the milk and vanilla. Set both mixtures aside.
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Working with a stand mixer fitted with the flat beater or working in a large bowl with an electric hand mixer, beat together the butter, sugar, and salt, first on low speed until combined, then increase the speed to medium and beat until fluffy and lightened in color, about 3 minutes. For a visual of what this should look like, see our video, how to cream butter and sugar.
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Add the eggs one at a time, beating well after each addition, about 30 seconds. Scrape down the bowl thoroughly.
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Add half of the flour mixture to the batter, beating gently to combine. Gently beat in the milk. (It’s OK if the batter looks curdled at this point.) Stir in the remaining flour until everything is well combined; the batter won't be entirely smooth but there shouldn’t be any large lumps.
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Use a flexible spatula to gently stir the berries into the batter by hand until they’re evenly distributed.
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Spoon the batter into the prepared pan, smoothing the top with a small offset spatula or the back of a spoon.
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Bake the Bundt cake for 45 to 60 minutes, or until a toothpick or thin knife inserted into the center comes out clean; tent with foil as necessary to prevent overbrowning.
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To make the glaze (if using): While the cake is baking, prepare the glaze. In a small bowl or liquid measuring cup, stir together the sugar, lemon juice, and vanilla.
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Remove the Bundt cake from the oven. Place the pan upside down on a cooling rack. If the cake drops out of the pan onto the rack, remove the pan. If the cake doesn’t drop onto the rack immediately, let it rest upside down for 5 minutes, then carefully lift the pan off the cake. If the cake feels like it's sticking, give it another 5 minutes upside down, then very gently shake the pan back and forth to loosen and remove it.
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Brush the glaze all over the hot cake, both the top and sides. Let the glaze sink in, then brush on more glaze, continuing until all the glaze is used.
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To make the berry icing: While the cake cools, make the icing. In a small saucepan, combine the berries and water. Bring to a simmer, then cook, smashing and stirring, until the berries have broken down, about 5 minutes. Strain the mixture through a fine-mesh sieve and into a liquid measure.
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Measure 3 tablespoons (43g) of the berry juice and transfer to a medium bowl (save or discard any excess).
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Whisk the confectioners’ sugar into the berry juice to create a thick glaze that's just barely pourable. Drizzle it over the completely cool cake, then let set until dry, about 30 minutes. Slice and serve the Bundt cake with lightly sweetened whipped cream, if desired.
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Storage information: Store the Bundt cake, well-wrapped at room temperature, for several days.
