In a large pot over medium heat, add a splash of olive oil and slowly sauté chopped leeks, onions, shallots, and minced garlic for about 10 minutes until soft.

Add diced Yukon Gold potatoes and vegetable broth to the pot, ensuring enough liquid covers the ingredients. Bring to a simmer over medium-high heat and then reduce to low. Cook for about 20 minutes until potatoes are tender.

Stir in chopped asparagus and sweet peas and cook for another 5 minutes, keeping the asparagus vibrant and just tender.

Gently mash some of the cooked potatoes against the pot's sides with a fork or masher to thicken the chowder.

Reduce the heat to low and stir in heavy cream or coconut milk and fresh dill. Cook for an additional 2 minutes to warm through.

Season with salt and pepper to taste. Ladle into bowls and serve hot with crusty bread or a salad.