Preheat oven to 425 degrees. Divide sweet potatoes and garlic between 2 baking sheets. Drizzle with 3 tablespoons olive oil and season with salt and pepper. Toss to coat and spread into a single layer. Roast, flipping once, until sweet potatoes are tender, about 30 minutes.
Meanwhile, bring 2 cups of water to a boil in a medium saucepan. Add farro, bring to a boil, then simmer and cook until tender, around 30-35 minutes. Drain water, place in a large bowl and drizzle with remaining 2 tablespoons of olive oil, toss to coat, season with sea salt and pepper.
When cool enough to handle, remove roasted garlic from peels and mash with lemon zest and lemon juice in a small bowl.
Add garlic/lemon mixture, sweet potatoes, dill and purple cabbage to farro and stir until well combined.