Preheat the oven to 450 degrees F. Arrange the blueberries on a baking pan lined with parchment paper. Toss with 1 tbs sugar and roll to coat.
Bake the berries for 20 minutes, checking and stirring as needed. Remove from oven and cool completely.
Reduce the heat to 350 F. Mash the graham crackers into coarse crumbs. Combine the graham cracker crumbs, brown sugar, butter, and salt in a bowl. Using your fingers, toss to combine so that the crumbs are all moist. Arrange on a parchment lined baking pan and toast, 8 to 10 minutes. All to cool.
When the berries and graham crackers have cooled, churn the frozen yogurt with remaining sugar in your ice cream maker according to manufacturers directions (took about 14 minutes for me). In the last minute, add the blueberries and graham crackers (I saved some and folded them in layers as well.
Pour into a resealable container and freeze 6 hours to overnight before scooping out and enjoying!