Heat the olive oil in a large pot over medium heat. Add the diced onion, sliced leeks, and minced garlic. Cook for 5 minutes until the vegetables soften.
Stir in the diced potatoes, dried thyme, salt, and black pepper. Cook for another 2 minutes to coat everything.
Pour in the vegetable broth. Bring the mixture to a boil, then reduce to a simmer. Cook for 15 minutes until the potatoes are tender.
Add the frozen chopped greens and the almond milk. Simmer for 5 more minutes until the greens are heated through and the chowder thickens slightly.
Taste and adjust salt and pepper if needed. Serve hot.