Preheat the oven to 350 degrees F (175 C).
Prep the aromatics: Peel the shallots, drizzle with 2 tablespoons oil, and wrap in foil. Peel the ginger, slice thinly, drizzle with 2 tablespoons oil, and wrap in foil. Pull outer paper off garlic, cut pointy tops off, drizzle with 2 tablespoons oil, and wrap each head in foil.
Bake the aromatics: Place all foil packets on a baking sheet. Bake for 15 minutes. Remove ginger (it should be soft), increase temperature to 400 F (200 C), and roast shallots and garlic for another 30 minutes until golden brown and fragrant. When cooled, squeeze garlic cloves out of paper.
Soak the chilis: While aromatics roast, pour boiling water over chili peppers to rehydrate. Let them soak for 15 minutes. Drain the water.
Make the paste: Combine roasted shallots, garlic, ginger, rehydrated chilis, salt, turmeric, mild curry powder, roasted ground coriander, and lemongrass paste in a food processor or blender. Add a splash of avocado oil if needed. Blend until a smooth paste forms, scraping down sides as necessary.