For the blackberry dressing: Mix the blackberries with the salt and leave at room temperature, covered, for 2 days.
Pour blackberries through a strainer or chinois sitting over a mixing bowl. Using the back of a ladle, press all juice and pulp through. Combine approximately 1 cup of the fermented blackberry juice with the blackberry vinegar.
For the avocado confit: Preheat the oven to 350 degrees F.
In a medium saucepan, bring oil to a low simmer. Add the onions and garlic and gently steep them in the oil, about 10 minutes. Meanwhile, season avocados with salt and Piment d'Espelette and place cut-side down in an even layer in a baking dish. Pour oil with onions and garlic over avocados and bake until soft, about 15 minutes.
To assemble: Arrange avocado confit in a large serving bowl along with the cooking oil, onions, and garlic. Drizzle blackberry dressing over top. Serve on grilled bread, garnished with fresh blackberries.