Preheat the oven to 350 degrees Fahrenheit and line an 8” x 8” square pan with parchment paper. If you don't have parchment paper on hand, you can spray the square baking pan with cooking oil, but the parchment paper makes for very easy removal of the bars from the pan post-baking.
In a large bowl, stir together the dry ingredients for the shortbread crust and topping (gluten-free all-purpose flour, oats, granulated cane sugar, and sea salt) until combined. Pour in the melted coconut oil (or avocado oil or melted butter) and stir the crumb mixture until a thick dough forms. Note: if you prefer using your food processor or a stand mixer with the paddle attachment instead of a mixing bowl, feel free to do so!
Reserve ½ cup of this crumble mixture to use as topping. Transfer the rest of the dough to the prepared baking dish and press it into an even layer using your hands or the back of a wooden spoon. You want the crust to be firmly pressed into the bottom of the pan so that it holds together nicely when sliced into bars. Poke the crust several times with a fork.
Bake the crust on the center rack of the preheated oven for 15 to 18 minutes, or until it is just slightly golden brown.
While the crust is baking, prepare the raspberry filling mixture. Transfer the raspberries and sugar to a saucepan and cover it with a lid. Heat over medium heat on the stovetop until the raspberry juices begin boiling. Use a fork to mash the raspberries, then stir in the gluten-free all-purpose flour until it is completely dissolved. Remove the raspberry filling from the heat. Set it aside until ready to use. The raspberry filling should resemble a thick fruit filling, similar to the consistency of stirred raspberry jam, yet not as thick as raspberry preserves.
Once the crust has finished pre-baking, remove it from the oven and pour all of the raspberry filling mixture over it, spreading it into an even layer.
Crumble the remaining dough over the raspberry layer. Bake the raspberry bars for 22 to 30 minutes, or until the crumble topping begins to show a little color.
Remove the bars from the oven and allow them to cool to room temperature. Store the bars covered with plastic wrap in the refrigerator until you’re ready to serve them. This refrigeration helps the bars to set up so that they slice nicely.
Transfer the raspberry oatmeal bars to a cutting board and use a sharp knife to slice them into squares. You can enjoy the bars at this point or whip up the optional glaze to drizzle on top.
To prepare the glaze, stir 1 cup of powdered sugar with 2 tablespoons of water or lemon juice in a small bowl until the sweetener is dissolved and a creamy glaze results.
Drizzle the glaze over the bars, and enjoy!