Prepare all the vegetables and aromatics: Wash the asparagus, cut off the woody ends, cut it into 1 inch (3 cm) pieces. Dice the onion, cut the garlic into thin slices. Peel the potatoes cut them into 1-inch (3 cm) chunks.
Cook: In a large pot, heat the oil, add the onion and thyme (if using dried), cook for about 5 minutes over low heat until soft and translucent. Add the garlic and cook for about 30 seconds, until fragrant. If you‘re using fresh thyme add it with the garlic. Transfer the onion and garlic to a plate.
Add the potatoes (you can add a little more oil if necessary) and cook for about 5 minutes over high heat, stirring from time to time, until nicely browned.
Simmer: Add the onion and garlic back to the pot, then add the asparagus and broth. Scrape with a spatula brown bits from the bottom of the pot. Simmer over low heat for about 10-15 minutes, until the asparagus and potatoes are tender.
Season: Take the pot off the heat, add the goat cheese and lemon juice (you can add a little less lemon juice now and after blending the soup add a little more to your taste, the soup should be just slightly sour). Using a blender, puree the soup until smooth, season with salt and pepper to taste.
Serve: You can serve the soup with the goat cheese sauce (just mix the goat cheese with lemon juice or milk together, drizzle over the soup) and toasted pumpkin seeds, but without these additions, it will still be very delicious.