Bring a large pot of salted water to a boil, then add the potatoes. Cook them until they're soft enough to poke with a knife or a fork, about 15 minutes. Strain and set aside.
Preheat the oven to 425°F and grease or line a baking sheet with parchment paper. Transfer the potatoes to the baking sheet. (You may need two baking sheets.) Using a fork or a potato masher, press each one down until it's smashed open. Drizzle with oil, sprinkle with sea salt then bake in the oven for 25-30 minutes, until golden brown and crispy on top.
Meanwhile make the avocado aioli by combining all of the ingredients in a food processor and blending until smooth. Add water or more lemon juice if a thinner texture is desired. Serve the potatoes warm with the avocado aioli and fresh dill.