Prep the corn. Cut kernels from cobs and set aside. If using fresh corn, leave them whole — you don't need to chop them further.
Cook the aromatics. In a large pot (at least 6-quart), melt butter over medium heat. Add diced onion with a pinch of salt and cook until softened and translucent, about 5 minutes. Stir in garlic and cook for another minute until fragrant.
Make the roux. Sprinkle flour evenly over the onions and stir constantly for 1 minute — you want it golden but not browned. This is what thickens your chowder.
Add the dairy. Slowly pour in the heavy cream while whisking to prevent lumps, then add the milk. Bring just to a simmer (do not boil), stirring occasionally, until the mixture has slightly thickened, about 5 minutes.
Cook the corn off-heat. Turn off the heat and stir in all of the corn kernels. This is the trick — cooking them gently without boiling preserves their sweet crunch. Let sit for 3–4 minutes so they warm through.
Add the cheese. Remove pot from heat entirely, then fold in 1½ cups cheddar and ¾ cup gouda. Stir until melted and creamy. Taste and adjust salt — you want it slightly under-seasoned since it'll be rich.
Finish and serve. Ladle into bowls, top with remaining cheese if desired, and garnish with chives. Serve immediately while hot.
To store: Transfer to an airtight container and refrigerate for up to 4 days. Reheat gently on the stovetop over low heat, stirring frequently — avoid boiling or your cheese may separate.
