Preheat oven to 350 degrees. Line a standard muffin pan with cupcake liners.
Place the apricots in a heat proof bowl and cover with boiling water. Let sit for 5 minutes.
In a large mixing bowl, whisk together the flour, baking soda, and salt. Make a well in the center.
In another mixing bowl, combine the sugar, buttermilk, butter, and egg. Add the wet ingredients to the dry ingredients and mix just until combined. Drain the apricots and fold into the batter.
Divide the mixture evenly among the prepared muffin tins. Top with the turbinado sugar. Bake for 20 minutes or until a toothpick inserted into the center comes out clean. Let cool in the pan for 5 minutes.