Make the cake:
Position a rack in the center of the oven and heat the oven to 350°F. Butter the sides and bottom of a 9x2-inch round cake pan. Fit a circle of parchment in the bottom of the pan and butter that as well.
Sift the flour, baking powder, and salt into a medium bowl. Whisk in the cornmeal; set aside.
Purée the corn kernels in a food processor until smooth. Strain the purée through a fine sieve, pressing with a rubber spatula to extract the liquid; scrape any purée off the bottom of the sieve into the liquid and then discard the remaining solids. Measure 1/4 cup of the strained corn liquid and transfer to a small bowl (discard any excess liquid). Stir in the sour cream.
In a stand mixer fitted with the paddle attachment, beat the butter and sugar on medium-high speed until fluffy, about 2 minutes. Stop and scrape the sides of the bowl. On low speed, slowly pour in the beaten eggs, mixing until incorporated and stopping midway to scrape down the sides. (The mixture will be loose and curdled-looking.)
On low speed, add one-third of the flour mixture and mix until just blended. Add one-third of the sour cream-corn mixture and mix until just blended. Alternate adding the remaining flour and sour cream mixtures in two additions each. Do not overmix.
Scrape the batter into the cake pan and spread it evenly with a spatula. Bake until the cake is golden brown and springs back when lightly pressed in the center, 30 to 35 minutes. Transfer to a rack to cool for 10 to 15 minutes. Run a knife around the edge of the pan and then gently invert the cake onto the rack, removing the pan. Remove the parchment, turn the cake right side up onto the rack, and let cool completely.
Make the compote:
Combine the sugar and 2/3 cup water in a small saucepan. Bring to a simmer over medium-high heat, stirring frequently until the sugar has dissolved completely. Remove from the heat. Add the lavender and stir to combine. Let infuse for 10 minutes, then strain the syrup into a small bowl and let cool.
When ready to serve the cake, stir the corn and blueberries into the syrup. Cut the cake into wedges, and top each serving with about 3 Tbs. of the mixture, letting most of the syrup drain off the spoon before sprinkling the blueberries and corn over the cake.