Make ahead: Preheat the oven to 350 °F. Drain 1 pound canned apricots.
Prepare the streusel: Put ⅓ cup all-purpose flour and ¼ cup granulated sugar into a medium bowl and add ⅓ stick unsalted butter cut into pieces. Combine with your fingers and create uneven crumbles.
Grease the baking dish with a ½ Tablespoon butter and dust with 1 Tablespoon flour.
Combine the dry ingredients: flour and baking soda.
Crack the eggs into a large bowl. Whip them with an electric hand mixer on high speed, gradually adding granulated sugar (not all at once, as you would choke up the batter). Continue whipping this mixture until you have used up all the sugar; the egg mixture will slowly get bigger, thicker, and lighter. It takes about 7-10 minutes until the eggs turn foamy.
Set the electric mixer to low speed. Little by little, add the oil, buttermilk, and flour mixture to the whisked eggs.
Pour the batter into a prepared pan. Put the apricot halves (or roughly chopped apricots) on top of the cake, and sprinkle with a thick layer of crumb topping.
Put the apricot cake into the preheated oven on the middle wire rack and let it bake for around 30-40 minutes. Once its surface turns golden brown, you are done.
Notes
The basic recipe makes about 12 portions.
I used a 13-inch (34 cm) round baking pan.
SERVING: Let the apricot cake cool, slice, and serve it for breakfast or brunch with a cup of coffee or tea.
If there is anything left over, cover them with plastic wrap and store it in the fridge. Here, this moist cake will keep for up to five days.