1. Preheat the oven to 375 degrees F. Adjust the rack to the middle position.
2. Trim the sprouts and halve them. I like to actually shave/thinly slice some and keep some halved, for variation of size and texture. Add about 3 to 4 tablespoons of oil to a large skillet over medium heat. Working in two batches, cook the Brussels sprouts cut side down, adding more oil as needed, until they are deeply browned (about 5 – 6 minutes). Flip them, season with salt and pepper, and cook for a few more minutes, or until you love how they look.
3. Transfer to a platter and arrange the sliced apples all around, just using as much or as little as you like. If it’s a big apple, half will probably do.
4. Meanwhile, make 6 equally sized mounds of the shredded cheese on a large baking sheet, keeping them a few inches apart, as they will flatten out as they cook. They don’t need to be perfectly shaped, just round-ish is fine. Bake for about 5 minutes (keep an eye on them) or until they are totally flat and almost doily-esque and lacey around the edges. Allow them to cool completely, tear them into big pieces, and arrange them all over the platter.
5. Sprinkle with poppy seeds and either 1) Toss with some of the dressing or 2) Serve with the dressing on the side (see below)

For the dressing

1. Combine all ingredients in a bowl and whisk to emulsify and thoroughly combine. Season to taste with salt and pepper, and adjust any ingredients to suit.