Place carrots, butternut squash, white and red sweet potatoes, and potatoes in separate containers. Add water to cover; let soak for several minutes. Drain.
Pour olive oil into large mixing bowl; add all the vegetables (not the apples) and toss to coat. Stir in 3/4 teaspoon Diamond Crystal(R) Fine Sea Salt, thyme and red pepper flakes. Spread vegetables evenly on a 12x18-inch rimmed sheet pan.
Bake 30 minutes; stir vegetables and add the apple pieces. Continue to bake for 30 minutes; stir again. Bake until vegetables and apples are brown and tender, about 20 more minutes.
Transfer to serving dish; garnish with torn flat leaf parsley and remaining Diamond Crystal(R) Fine Sea Salt.