Preheat the oven to 350°F. Grease a 9-inch deep dish pie dish, an 8-inch or 9-inch springform pan, or an 8-inch square baking pan.
Make the batter: In the large bowl of your stand mixer with paddle attachment (or using a hand mixer), cream the butter and granulated sugar together on high speed until smooth and creamy, about 2 minutes. Scrape down the sides and up the bottom of the bowl with a rubber spatula as needed.
Add the eggs, sour cream, vanilla extract, and almond extract. Beat on medium-high speed until combined. The mixture may look curdled, and that’s okay, but I like to add a couple tablespoons of flour at this stage to help it come together. Scrape down the sides and up the bottom of the bowl as needed.
Gently beat in the dry ingredients (flour, baking powder, cinnamon, and salt) on low speed, until smooth and just combined---don't overmix. The batter will be thick (which is good).
With your rubber spatula, carefully fold in the cherries and apricots (again, do not overmix).
Spoon and spread into the prepared pan and set aside while you make the crumb topping.
Make the crumb topping: Melt the butter in a small bowl and then with a fork, mix the flour, brown sugar, and cinnamon into the butter. Stir until crumbs form, but don't overmix and turn it into a paste. You want it crumbly!
Sprinkle the crumb mixture and sliced almonds evenly on top of batter.
Bake for 45-60 minutes. Baking times vary, so keep an eye on yours. If you use an 8-inch springform pan (which I did), it will take even longer. The buckle is done when a toothpick inserted in the center comes out clean and you can't hear it kind of "sizzling" anymore. You definitely don't want it too gooey in the middle. If you find the top of the buckle is browning too quickly in the oven, loosely cover it with aluminum foil.
Remove from the oven and set it on a wire rack. Cool for at least 15 minutes before removing from the pan and slicing. I like to let it cool completely and kind of "set up".
Cover leftovers tightly and store in the refrigerator for up to 5 days (I'll be honest, I often keep on the counter...). This is best the next morning, but not as great after about 2 days, so there's your sweet spot.