Preheat and prep the pan: Heat oven to 350°F using top and bottom heat. Line a 9-inch square baking pan with parchment paper, letting it hang over the edges slightly.
Whip eggs, sugar, and vanilla: In a large bowl, whisk 3 large eggs, 0.5 cups granulated sugar, and 1 teaspoons vanilla extract together until light in color and slightly thickened.
Add yogurt and oil: Add 0.5 cups plain Greek yogurt and 0.4 cups sunflower oil (or canola oil) to the egg mixture. Mix until completely smooth with no streaks of oil remaining.
Fold in dry ingredients: In a separate bowl, stir together 1.5 cups all-purpose flour, 2 teaspoons baking powder, and 1 pinch salt. Fold into the wet batter gently until just combined — do not overmix.
Pour the batter: Pour the batter into the prepared pan and smooth the top into an even layer with a spatula.
Pipe and swirl the jam: Transfer 3.5 tablespoons apricot jam (apricot preserves) into a piping bag (or zip-top bag with corner snipped). Pipe thin lines across the batter, then gently drag a skewer through the lines to create a soft marble swirl.
Add apricot cubes and almonds: Evenly scatter 7 canned apricot halves, well drained and cut into small cubes over the batter, then sprinkle with 2 tablespoons chopped almonds.
Bake the cake: Bake at 350°F until golden brown and a toothpick inserted in the center comes out clean.
Cool and dust with sugar: Let the cake cool completely in the pan, then lift out using the parchment edges. Dust with 1 tablespoons powdered sugar, for dusting (optional) before slicing and serving.