Melt the butter in a large pot over medium heat. Add the onion, celery, and jalapeño; cook for 3 minutes or until tender, stirring frequently.: The air will fill with a warm, dairy scent as the butter melts into a glossy pool. Listen for the faint hiss as it reaches temperature, avoid browning it; you want a pale, fragrant base. This gentle start creates a smooth mouthfeel later, and rushing with too-high heat can burn the fat, introducing bitter flavors. If you see dark specks, wipe the pot and start over to preserve the chowder's clean taste.
Add in the flour; cook 1 minute, stirring constantly. Stir in the milk and remaining ingredients.: As the diced onion and celery soften, they release sweet and herbal aromas while the jalapeño contributes a green, peppery brightness. You should notice the onion turn translucent and the celery losing rigidity; that is the visual cue the flavors are marrying. Stirring frequently prevents sticking and ensures even softening. A common mistake is overcrowding the pot, which steams rather than sautés, leaving raw-tasting vegetables; if your pan seems crowded, cook in two batches.
Bring to a boil, and cook until thickened (about 5 minutes.): When the all purpose flour is added, it will form a paste with the butter and vegetables. Cook just until it smells slightly toasty and the raw flour aroma is gone; this helps the chowder thicken without tasting pasty. Stir constantly to avoid lumps, scrape the bottom so nothing sticks, and watch the color; it should remain pale. If you see clumps, use a whisk and a splash of the milk to smooth them out before adding all the liquid.
Stir in the milk and remaining ingredients: Pour in the milk gradually while whisking or stirring to create a smooth, velvety base. Then add the canned cream style corn , frozen or fresh corn , chopped roasted skinless, boneless chicken , chopped fresh thyme , salt , and ground red pepper . You should see the mixture come together into a pale, slightly speckled liquid with bits of corn and herbs. The milk will mellow the roux while the cream style corn contributes sweetness and body. If the mixture looks too thin at this point, a few minutes of gentle simmering will thicken it; if too thick, add a splash more milk .
Bring to a boil, and cook until thickened about 5 minutes: As the pot comes to a boil, bubbles will rise steadily and steam will carry the scent of corn and thyme . Reduce to a gentle boil and watch as the liquid thickens, coating the back of a spoon; that is the texture you want. The corn kernels should become tender but still offer slight bite, while the chicken warms through and blends with the savory base. A frequent error is overboiling, which can separate the dairy and flatten the flavors, so keep heat moderate and stir occasionally. When the chowder clings to a spoon and has a creamy sheen, it is ready to serve.