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Preheat oven to 475 degrees Fahrenheit.
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Line a baking sheet with foil, and place bacon strips flat on baking sheet.
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Roast bacon for 10–12 minutes. (Keep an eye on it to make sure it doesn’t burn.)
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Place bacon on a plate lined with paper towels to soak up the excess grease, and set aside.
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Add olive oil, onions, garlic, and red bell pepper to a large stock pot over medium heat, stirring to coat. Saute until onions are translucent (about 5 minutes).
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Add in broccoli florets and salt, and continue sauteing for another 2–3 minutes, stirring to incorporate all ingredients.
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Add in bone broth and apple cider vinegar, lower the heat, and cover for 5 minutes.
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Add in cream cheese, stirring with a fork or whisk to break it up and allowing it to melt into the broth.
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Use an immersion blender to pulse through the vegetables. Coarsely blend for larger broccoli chunks, or blend more thoroughly for a more uniform soup.
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Slowly add shredded cheddar cheese, bit by bit, stirring the whole time to avoid chunks of cheese forming or clumping.
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Stir in heavy cream and cook on low, stirring occasionally for 7–10 minutes more to allow the soup to thicken.
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Top with crumbled bacon, chopped scallions, and extra shredded cheese and serve piping hot.