In a large pot, heat olive oil over medium heat. Add diced onion and sauté until translucent, about 5 minutes. Stir in minced garlic and cook for an additional minute until fragrant.
Pour in the crushed tomatoes and vegetable broth. Add dried basil, oregano, salt, and pepper. Bring to a simmer and let cook for 15 minutes.
Remove the pot from heat and stir in the heavy cream. Use an immersion blender to puree the soup until smooth, or carefully transfer to a blender in batches. Return to low heat to keep warm.
For the dumplings, preheat the oven to 425°F. In a large bowl, whisk together flour, baking powder, garlic powder, and salt.
Cut in the cold butter until the mixture resembles coarse crumbs. Stir in shredded cheddar cheese.
Gradually add milk to the flour mixture, stirring until just combined. Do not overmix.
Drop spoonfuls of the dumpling batter onto the simmering soup. Cover the pot and let cook for 15 minutes, or until the dumplings are fluffy and cooked through.
Serve the soup hot, garnished with fresh parsley if desired.