In a stockpot, melt the butter over medium heat. Add the leek and garlic. Cook until tender, about 5 minutes. Stir to prevent them from browning.
Add the potatoes and stock. Bring to a simmer. Cook for 5 minutes.
Add the broccoli and asparagus. Simmer for an additional 10 to 12 minutes until the vegetables (including the potato) are fork tender.
Carefully transfer soup to a blender and process until smooth. Work in batches if needed.
Pour the soup back into the pot, place on low heat, and stir in lemon juice. Break the goat cheese into pieces and stir into the soup. Whisk until melted. Season to taste.
Ladle into bowls and top with fresh chives.
Notes
Vegetable broths and stocks vary greatly on sodium content and other seasonings. Wait until the end to add salt and pepper.
Leftovers: Store in an airtight container in the fridge for 3-4 days or in the freezer for up to 3 months.