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Set a large Dutch oven or stockpot over medium heat. Add bacon and cook until crisp, about 5 minutes.
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Add onion and celery, cook for 3 minutes, then add corn and continue cooking for an additional 4 minutes. Add garlic and cook until fragrant, about 1 minute.
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Pour in chicken broth and turn the heat up to medium-high. Once the mixture is simmering, add the potatoes along with the salt, pepper, paprika, parsley, thyme, and cayenne. Reduce heat to medium and cook for 10 minutes before adding the zucchini and yellow squash.
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Once the zucchini and yellow squash have been added, cook until the potatoes are fork-tender and the zucchini and squash are fully cooked, about 10-12 minutes.
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Transfer 2 cups of chowder to a food processor or blender. Puree until silky smooth, about 1-2 minutes. Return the mixture to the pot and add the half and half. Stir to combine, then remove from the heat.
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Let the chowder sit for 10 minutes before serving.