In a large pot, heat the olive oil over medium heat. Add the diced onion and sauté until translucent, about 5 minutes.
Add the minced garlic and sauté for an additional minute until fragrant.
Stir in the pumpkin puree and diced tomatoes. Cook for 2-3 minutes, allowing the flavors to meld.
Pour in the vegetable broth, and add the dried basil, oregano, salt, and black pepper. Bring the mixture to a boil.
Reduce the heat and simmer uncovered for about 20 minutes, stirring occasionally.
Using a blender or immersion blender, carefully puree the soup until smooth. Return the soup to the pot and keep warm.
While the soup is cooking, make the grilled Swiss cheese sticks. Heat a grill pan or skillet over medium heat.
Butter one side of a slice of bread, and place it butter-side down on the pan. Top with 2 slices of Swiss cheese, then place another slice of bread on top (butter-side up).
Grill for 3-4 minutes on each side until the bread is golden brown and the cheese is melted. Remove and cut into sticks. Repeat with remaining ingredients.
Serve the warm pumpkin tomato soup in bowls with grilled Swiss cheese sticks on the side.