Preheat oven to 400°. Line a rimmed baking sheet with parchment paper. Spray 2 (8-inch) square cake pans with baking spray with flour.
In a medium sauté pan, heat ½ tablespoon olive oil over medium heat. Add onion; cook until edges begin to char. Transfer to a heatproof bowl. Let cool completely.
In a large bowl, whisk together sautéed onion, flour, cornmeal, Parmesan cheese, sugar, baking powder, thyme, and 1 teaspoon salt.
In a medium bowl, whisk together buttermilk, melted butter, and eggs. Fold buttermilk mixture into onion mixture until combined. Divide batter between prepared pans.
Bake until a wooden pick inserted in centers comes out clean, 20 to 25 minutes. Let cool completely on a wire rack.
In a small saucepan, melt butter over medium heat. Cook until butter turns a medium-brown color and has a nutty aroma, approximately 5 minutes. Pour browned butter into a heatproof bowl.
Remove cooled cornbread from pan. Using a 2¼-inch fluted square cutter, cut 18 squares from cornbread, discarding scraps. Brush tops of cornbread squares with browned butter.
In a medium heatproof bowl, stir together bread crumbs, red pepper, black pepper, and remaining ½ teaspoon salt.
In a medium sauté pan, heat remaining 1 tablespoon olive oil over medium-high heat. Add green beans; cook until beans darken, 2 to 3 minutes. Add green beans to bread crumbs mixture, stirring until beans are coated. Let cool slightly.
Divide green beans among prepared cornbread squares. Serve immediately.
Recipe by TeaTime Magazine at https://teatimemagazine.com/cornbread-canapes-with-crispy-green-beans-recipe/