Great cook, great baker. Really good instructions on her web site: alexandracooks.com

1⁄2 cup (8 tablespoons|1 stick| 4 oz | 113 g ) unsalted butter, room temperature 

zest from 1 large lemon

1 cup (214 g) sugar (set aside 1 tablespoon for sprinkling)

1 egg, room temperature

1 tsp. vanilla

2 cups (256 g) all-purpose flour (set aside 1/4 cup of this to toss with the blueberries) 

2 tsp. baking powder

1 tsp. kosher salt (I like 1.25 tsp)

2 cups fresh blueberries, picked over

1⁄2 cup buttermilk, see FAQs below

1. Preheat the oven to 350oF. Using a stand mixer or hand-held mixer, cream the butter with the lemon zest and the 1 cup minus 1 tablespoon of sugar until light and fluffy.

2. Add the egg and vanilla and beat until combined. Meanwhile, toss the blueberries with 1⁄4 cup of flour, then whisk together the remaining flour, baking powder and salt.

3. Add half of the flour mixture to the batter, and stir with spatula to incorporate. Add all of the buttermilk. Stir. Add remaining flour, and stir until flour is absorbed. Fold in the blueberries. (Leave excess flour from the blueberry bowl behind.)
 

4. Grease an 8- or 9-inch square baking pan (or something similar—I prefer this 8-inch pan because I like the thicker pieces) with butter or coat with non-stick spray. If you have parchment paper on hand, line the pan with parchment on top of the butter. Spread the batter into the pan. Sprinkle the batter with the remaining tablespoon of sugar. Bake for 35 to 45 minutes — a 9-inch pan will be done in closer to 35 minutes; an 8-inch pan usually needs 40 to 45 minutes. Check with a toothpick for doneness. If necessary, return pan to oven for a couple of more minutes. (Note: Baking for as long as 10 minutes more might be necessary, especially if you’re using a smaller pan such as an 8×8-inch. It’s not unusual for this cake to take 50 minutes, so just be patient.) Let cool at least 15 minutes before serving.

Can this be doubled? Yes. Bake it in a 9×13-inch pan ... like this pan from Pyrex. Increase the baking time but begin checking at the 35 minute mark.

What if I don’t have buttermilk? Use 2% or whole milk or make your own buttermilk: place 2 teaspoons of vinegar or lemon juice in a liquid measuring cup. Fill cup with milk until it reaches the 1/2-cup line. Let stand for five minutes. Use as directed.

Can this be made gluten free? Yes. I like Cup4Cup and King Arthur Flour gluten-free flour mixes, but use whatever you like, keeping in mind that all gluten-free flours absorb liquid differently, so you may need to adjust to get the batter to the right consistency.

Should the batter be thick? Yes. As with all baking, I highly recommend using a scale to measure the flour. 

Can I bake this into muffins? Yes. Follow the baking directions on this post. 

Can I use frozen berries? Yes. No need to thaw.

What other fruit could I use? Really any fresh fruit or berries. Around the winter holidays, I make this cranberry-orange buttermilk breakfast cake.

Can this be frozen? Made ahead of time? Yes! Let cool completely, then wrap well with plastic wrap or other airtight wrap. Freeze for up to 3 months. Let thaw at room temperature the night before serving. Reheat at 350ºF for 15 minutes before serving. If you are not freezing it, store it at room temperature for a day. Refrigerate if storing for more than 1 day.

Find it online: https://alexandracooks.com/2011/06/29/buttermilk-blueberry-breakfast-cake/