Heat olive oil in a medium pot over medium heat. Sauté onion and garlic until fragrant.
Add chopped zucchini, cook for 5 minutes, stirring occasionally.
Pour in vegetable broth, bring to a simmer, and cook 10 minutes until tender.
Blend soup until smooth, then stir in plant milk. Season with salt and pepper.
For pudding, whisk cornstarch with a small amount of oat milk until smooth.
Heat remaining oat milk, coffee, and maple syrup in a saucepan.
Slowly add cornstarch mixture while whisking. Cook until thickened, about 5 minutes.
Remove from heat, stir in vanilla and salt, then chill pudding while serving soup.