Heat your large pot on medium heat.
Once it is hot, add butter and olive oil to the pan. Melt butter and mix together with olive oil.
Next, add roughly chopped onions to the pot and sauté until the onions are translucent.
Add the chopped garlic to the pot and let it warm through. Season with salt, pepper, and a sprinkle of chili flakes.
Turn off the heat.
Blending with a regular blender
Place the sautéed onions and garlic into the blender with canned tomatoes and basil leaves.
Place the lid on and blend on high until completely smooth. If the mixture is too thick add a small amount of broth to the blender, and blend on high until smooth.
Blending with an Immersion Blender
An Immersion blender can be used right inside the pot on the stove top.
Make sure the heat is off. Add canned tomatoes, basil leaves, and broth to the soup pot.
Place the immersion blender into the pot. Make sure the end of the wand is fully submerged and then blend until smooth.
Do not blend hot liquid. Splashes of hot liquid an be very dangerous.
Bring the pot of blended tomatoes up to a low simmer.
Let it simmer on medium low heat for 10 minutes.
Then, add heavy cream and stir.
Simmer the tomato basil bisque for another 10 minutes.
Season with salt and pepper to taste.