Make your dressing. In a large bowl combine the olive oil, lemon juice, grated parmesan cheese, garlic, salt, and pepper. Whisk to combine and set aside.
Prep your ingredients. Wash and dry the brussels sprouts, cut off the stems at the base, and chop them in half lengthwise. With the flat side down, slice the brussels sprouts into thin rounds so they appear shredded. Next, peel the carrots and using a mandolin or knife, slice the carrots into 1/4 inch thick wide strips. Chop a honeycrisp apple in half and with the flat side down, slice the apple into thin pieces.
Heat 1 tablespoon of olive oil in a large pan on medium heat. Once shimmering, add the shredded brussels sprouts and carrot ribbons. Stir this mixture together for about 5-6 minutes or until the brussels sprouts start to turn golden brown in some spots.
Add the pistachios and apple slices and cook this mixture for another 3 minutes.
Turn the heat to low and pour in the dressing. Mix the dressing into the salad and let this cook for a few more minutes. Turn the heat off and transfer the salad to a large serving bowl.
Add in the dried cranberries and goat cheese. Toss to combine.
Serve warm!