Preheat the oven to 350°F (175°C). Grease an 8-inch cake pan and set aside.
In a small bowl, whisk together the all-purpose flour, baking powder, and salt until evenly combined.
In a large bowl, beat the 3/4 cup softened unsalted butter and 2/3 cup light brown sugar with an electric mixer on high until light and fluffy, scraping the bowl as needed.
Add the eggs one at a time, then the 1/2 cup canola oil and 2 teaspoons almond extract, mixing on medium until fully incorporated.
Fold in the 1/2 cup slivered almonds, then gradually add the flour mixture and mix until the batter is smooth and uniform.
Pour the batter into the prepared 8-inch pan and smooth the top. Bake on the center rack for 40–50 minutes, or until a toothpick inserted into the center comes out clean.
Remove the cake from the oven and cool in the pan on a rack for 15 minutes. Run a knife around the edge if needed, then transfer the cake to a serving plate to finish cooling slightly.
Make the brown-butter almond glaze: melt 1/4 cup unsalted butter in a small skillet over medium heat until it foams and turns a light amber color, then remove from heat and transfer to a bowl to cool slightly.
Whisk the 1 cup powdered sugar, 1/4 cup heavy cream, and 1 teaspoon almond extract into the browned butter until smooth.
Pour the glaze over the warm cake, sprinkle additional slivered almonds on top, and allow the glaze to set before slicing and serving.