In a large pot, heat olive oil over medium heat. Add diced onion and sauté until translucent, about 5 minutes. Add minced garlic and cook for an additional minute until fragrant.
Stir in the crushed tomatoes, vegetable broth, dried basil, dried oregano, sugar, salt, and pepper. Bring to a simmer and cook for 20 minutes, stirring occasionally.
Using an immersion blender, puree the soup until smooth. If you don’t have an immersion blender, carefully transfer the soup to a regular blender in batches.
Return the soup to the pot and stir in the heavy cream. Heat gently until warmed through, then adjust seasoning if necessary.
While the soup is simmering, preheat the oven to 425°F.
In a large bowl, whisk together the flour, baking powder, garlic powder, and salt. Stir in the shredded cheddar cheese.
In a separate bowl, combine the melted butter and milk. Pour the wet ingredients into the dry ingredients and mix until just combined.
Drop spoonfuls of the dumpling mixture onto a baking sheet lined with parchment paper. Bake for 12-15 minutes or until golden brown.
Serve the tomato soup hot, topped with the cheddar bay dumplings.