Preheat your oven to 350°F (175°C). Lightly butter or spray a 9×13-inch baking dish (or a similar 3-quart dish) to prevent sticking and help the edges brown.

In a large bowl, combine the sliced apricots, 1/2–2/3 cup granulated sugar, cornstarch, lemon juice, 1 teaspoon vanilla extract, almond extract (if using), and 1/4 teaspoon fine sea salt. Toss gently until the fruit is evenly coated and you no longer see dry cornstarch. A light, syrupy coating should form on the fruit.

Pour the apricot mixture into the prepared baking dish and spread it into an even layer. If possible, tuck most of the apricot skins facing down so the top bakes up more evenly golden.

In a medium bowl, whisk together the flour, 3/4 cup granulated sugar, baking powder, 1/4 teaspoon fine sea salt, and ground cinnamon (if using). In a separate bowl or large measuring cup, whisk the melted butter, milk or buttermilk, and 1 teaspoon vanilla extract. Pour the wet ingredients into the dry ingredients and stir just until combined. The batter should be thick but pourable, like a loose muffin batter; do not overmix.

Spoon the cobbler batter over the apricots in rustic dollops. You do not need to cover all of the fruit; leaving small gaps allows the apricot filling to bubble up and caramelize as it bakes.

Bake on the center rack for 35–45 minutes, until the topping is deep golden brown around the edges, lightly golden in the center, and the apricot filling is bubbling up around the sides and through some gaps. If the top browns too quickly before the filling is bubbling, tent the dish loosely with foil for the last 5–10 minutes.

Remove the pan from the oven and let the cobbler cool for 15–20 minutes. The filling will thicken as it rests, making for neater servings and a better texture.

Spoon the warm apricot cobbler into bowls. Serve plain or with vanilla ice cream, whipped cream, or a spoonful of plain or vanilla Greek yogurt.