Cook the barley according to package directions, typically simmering in boiling water for about 30 minutes until tender. Drain and set aside.

In a large pot, heat olive oil over medium heat. Add leeks, carrots, and shiitake mushrooms, sauté for 5-7 minutes until leeks are translucent.

Stir in garlic, parsley, dill, sea salt, and black pepper, cooking for an additional 2-3 minutes until fragrant.

Add cubed potatoes and stir to absorb flavors.

Pour in vegetable stock and water, increase heat to bring to a boil, then reduce to a simmer for about 10 minutes until potatoes are fork-tender.

Stir in cooked barley, chopped asparagus, vegan heavy cream, lemon juice, and lemon slices, cover, and simmer for 5 more minutes.

Remove from heat and gently stir in fresh spinach until just wilted, taste and adjust seasoning, then serve.