In a stock pot, heat the oil and add the onion, cooking until translucent, then add the thyme and garlic.
Season with salt, freshly ground black pepper, cayenne pepper and thyme leaves, and immediately add the stock; stir.
Bring stock to a boil, and add broccoli and mushrooms. Cover, lower heat to simmer and cook, stirring occasionally, for about 10-15 or until broccoli becomes tender (depends on the size of the broccoli pieces).
Whisk flour and paprika into a small bowl along with the evaporated milk. Stir into soup, and raise heat, stirring constantly. When soup comes to a boil, if your soup is thick as you like it finish by adding the cream and removing from heat. If it's a little thin for you, whisk some more flour in the heavy cream and add that, stirring until it boils and thickens.