Prep the pan and oven: Preheat the oven to 350°F (175°C). Grease a 9-inch round cake pan or springform pan and line the bottom with parchment.
Slice the plums: Halve and pit the plums, then cut into wedges about 1/2 inch thick.
Set aside.
Cream the butter and sugar: In a large bowl, beat the softened butter and 3/4 cup sugar until light and fluffy, 2–3 minutes. This traps air and helps the cake rise.
Add eggs and flavorings: Beat in the eggs one at a time, scraping the bowl. Add vanilla and lemon zest, if using, and mix until smooth.
Combine dry ingredients: In a separate bowl, whisk flour, baking powder, salt, and cinnamon.
Mix the batter: Add the dry ingredients to the butter mixture in two additions, alternating with the sour cream.
Mix just until combined. The batter will be thick.
Spread into the pan: Scrape the batter into the prepared pan and smooth the top with a spatula. It doesn’t need to be perfect.
Arrange the plums: Nestle plum wedges on top in a circular pattern, slightly pressing them into the batter.
Don’t overcrowd—leave small gaps for the batter to rise.
Sprinkle the top: Scatter 1–2 tablespoons sugar (and turbinado, if using) over the plums for a glossy, caramelized finish.
Bake: Bake for 40–50 minutes, until the edges are golden and a toothpick in the center comes out with a few moist crumbs. Juices may bubble around the fruit.
Cool: Let the cake cool in the pan for 15 minutes, then run a knife around the edge and transfer to a rack. Cool until just warm or room temperature.
Finish and serve: Dust with powdered sugar if you like.
Serve plain, with softly whipped cream, or a scoop of vanilla ice cream.