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In a large pot over medium-high heat, melt butter. Add in onions, carrots, and broccoli. Cook to soften for about 5 minutes.
Slowly add in broth, milk, and cream. Sprinkle with flour and add salt, pepper, and red pepper flakes. Continue stirring and heating over medium heat until thickened. This will take about 10-15 minutes.
Once thick, add cheese and stir until melted and smooth. Serve soup and enjoy!