Preheat oven to 350°F. Butter an 8-inch square cake pan and line with a square of parchment paper.
In a large bowl, beat ½ cup unsalted butter and ½ cup granulated sugar and ¼ cup brown sugar with an electric mixer at medium speed until pale and fluffy, then beat 2 large eggs 1 at a time, beating well after each addition. On low speed, beat in the 1 teaspoon pure vanilla extract and 1 cup buttermilk until just combined.
In a medium bowl, sift together 1 ¾ cup oat flour, ¼ cup almond flour, 1 ½ teaspoons baking powder, ¾ teaspoon baking soda, nd ½ teaspoon fine sea salt Add this mixture to the creamed mixture, mixing until just incorporated.
Spread batter evenly in cake pan and let rest for 20 minutes. Then, place in the oven and bake until the top of the cake is golden and a toothpick inserted in the center comes out clean, 35 to 40 minutes. Cool in pan on a rack for 10 minutes, then run a knife around the edge of the pan and invert onto rack to cool completely (about 1 hour).
Make Glaze
Bring 1 cup heavy cream, ½ cup brown sugar, and a pinch of salt to a boil in a heavy saucepan over medium heat, stirring until the sugar has dissolved. Boil until glaze registers 210 to 212°F on a candy thermometer, about 12 to 14 minutes, then stir in 1 teaspoon pure vanilla extract.
Put rack with cooled cake in a shallow baking pan and pour hot glaze over top of cake, allowing it to run down sides. Cool until glaze is set, about 30 minutes.
Notes
Have a candy thermometer handy. Caramel can be tricky, and the best way to ensure it's done is to use a candy thermometer. The caramel will be a nice pouring consistency when it reaches 212F on the candy thermometer. Pull it off the stove when you get this reading so that it doesn't overcook.
Dissolve the sugar fully. Don't start boiling the caramel until the brown sugar is fully dissolved. If it's not fully melted into the cream, the caramel can be grainy.
Cool the cake fully. Hot caramel over a hot cake is not a good idea! Cool the cake thoroughly - about 1 hour - before pouring over the caramel.
Let the caramel set. After pouring the caramel over the cake, use a knife to spread it out evenly. Then, let it cool and set for at least 20 minutes before serving. You can place the cake + caramel in the fridge to speed up this process.
Make it a layer cake. Double the recipe and bake in 2 9-inch cake pans. Use the glaze to top the cake, and make my salted caramel frosting to fill and frost the sides of the cake. Yum!