Preheat your oven to 400°F.
Line a baking tray with parchment paper. Place the chopped carrots on the tray, drizzle with olive oil, and season with salt and pepper.
Slice the top off the garlic head to expose the cloves. Drizzle olive oil over the exposed cloves, sprinkle with salt, and wrap the garlic in aluminum foil. Place the garlic on the baking sheet with the carrots. Roast in the preheated oven for 30-40 minutes, or until the carrots are fork-tender and golden brown.
While the carrots and garlic are roasting, prepare the fried shallots. Pat dry the shallots, then heat 2 tablespoons of oil in a medium-high heat pan. Add the shallots and cook, stirring frequently, until browned and crispy, about 10 minutes. Place them on a plate lined with paper towel and season with salt.
In a food processor, squeeze the roasted garlic cloves out of their skins. Add the beans, paprika, coriander, salt, olive oil, and roasted carrots. Process until smooth, then adjust the seasoning with salt and pepper to taste. If the dip is too thick for your liking, add a teaspoon of water and let the food processor run for a second or two to mix.
Transfer the dip to a serving platter and top with chopped dill, the crispy shallots, and sprinkle of sea salt and a drizzle of olive oil. Serve and enjoy!