Heat olive oil in a saucepan; sauté onion and garlic until soft.
Add tomatoes and cook until they break down, about 10 minutes.
Pour in vegetable broth; simmer 10 minutes.
Blend soup until smooth; stir in coconut milk, salt, and pepper.
Keep warm while preparing pudding.
Coffee Pudding:
In a bowl, mix cornstarch with a little almond milk to form a slurry.
Heat brewed coffee, remaining almond milk, and maple syrup in a saucepan.
Slowly whisk in cornstarch mixture; cook until thickened, about 5 minutes.
Remove from heat, stir in vanilla, and cool slightly.
Serving:
Spoon warm soup into bowls; add a dollop or side of coffee pudding. Garnish with fresh basil.