Place the broccoli in a food processor. Cover and process until finely chopped, about 5 seconds. Remove to a medium bowl.
Add the mixed vegetables and carrots to the processor bowl; process until finely chopped, about 5 seconds. Remove to the medium bowl.
In a large saucepan, heat the oil over medium-high heat. Add the butter and all chopped vegetables. Cook for 3 to 5 minutes, stirring frequently.
Stir in the garlic salt, thyme, and cayenne pepper. Cook for 3 to 5 minutes or until aromatic.
Stir in the flour until mixed. Add the stock and bring to a boil. Reduce the heat and add the milk. Simmer for 8 to 10 minutes or until vegetables are tender and the soup is slightly thickened.
Serve with shredded cheese and dollops of sour cream.