Using a high-speed blender, combine carrots, coconut milk, garlic, oil, lemon zest and juice, ginger, tomato paste, honey, water, and a few generous pinches of salt and pepper. Blend until completely smooth.
Taste and adjust seasoning.
Chill for at least 4 hours. If the soup thickens in the fridge, stir in a little more cold water.
To serve, ladle into bowls and top with garnishes as desired.
To toast pumpkin seeds: In a heavy, medium-sized skillet, heat 1 tablespoon extra-virgin olive oil over medium-high heat. Add seeds and stir until toasted, about 2 minutes.