Preheat oven to 350°F. Line a 9-inch round cake pan with parchment paper and lightly coat with nonstick spray.
Add ½ cup (113g or 1 stick) butter to a skillet over medium heat and cook, swirling occasionally, until browned and fragrant, about 8 minutes. Transfer to a heatproof bowl.
Whisk 1 ½ cups (180g) flour, 2 teaspoons (9g) baking powder, and ¾ teaspoon (5g) salt in a large bowl.
Whisk 3 eggs, 1 ½ cups (340g) cottage cheese, 1 cup (200g) sugar, 1 teaspoon (7g) vanilla and ½ teaspoon (4g) almond extract in a medium bowl until smooth and pale, about 1 minute; fold in dry ingredients just until combined.
Measure out ¾ cup sliced apricots and set aside. Fold in remaining apricots then fold in browned and cooled butter. Scrape batter into prepared pan and scatter reserved ¾ cup apricots over top. Pinch streusel into dollops and sprinkle evenly over top of batter.
Bake cake until golden brown, center does not jiggy when gently shaken and a toothpick inserted into center comes out clean, 60–70 minutes*, rotating pan halfway through. Let cool at least 20 minutes before flipping to unmold and then flipping again to serve.
Serve slightly warm with whipped cream.