Place bratwurst and beer in a large skillet over medium-high heat. Bring to a gentle simmer and cook for 10 minutes, turning once, until mostly cooked through. The beer will reduce by about half.

Remove bratwurst to a plate. Pour out all but a thin film of beer from the pan, add vegetable oil, and increase heat to medium-high. Return bratwurst to the skillet and sear for 2-3 minutes per side, turning until deeply browned and crisp in spots. Transfer to a plate and tent with foil.

In a large bowl, whisk together mayonnaise, Dijon mustard, honey, apple cider vinegar, celery seed, salt, and pepper until smooth and emulsified. Taste and adjust - it should be tangy-sweet with a mustard bite.

Add broccoli slaw mix to the bowl and toss thoroughly to coat every strand. Let sit for 5 minutes to soften slightly, then toss again. The slaw should be creamy but not swimming in dressing.

Divide slaw among plates, nestle bratwurst alongside, and serve warm. The contrast of hot, snappy sausage and cool, crisp slaw is the whole point.