Heat oven to 325°. Spread breadcrumbs on a baking sheet. Bake until crunchy, about 15–20 minutes. Allow to cool and store in an airtight container.
Rinse the cauliflower. Cut and trim florets enough to measure 2 cups and set aside. Chop remaining cauliflower, place in a medium saucepan and cover with whole milk. Add 1 teaspoon salt and several grinds of white pepper. Place over medium-low heat and allow to simmer until cauliflower is extremely soft and tender, about 20 minutes.
Gently scoop out pieces with a slotted spoon, and place into a high-speed blender, reserving the milk. Blend on high, and add milk just until the mixture is able to freely purée. The consistency should be between mashed potatoes and a creamy soup. Season to taste and keep warm. (Can be made in advance and reheated.)
Melt butter on high heat in a sauté pan until it foams lightly. Add the cauliflower florets to the pan and spread into a single layer. Allow to caramelize for 3–4 minutes, then turn to caramelize the other side. Once the cauliflower is soft but still lightly crunchy, remove from pan. Place on tray lined with paper towels. Season with salt and pepper and keep warm.
Thinly slice apples immediately before serving. To serve, place ½ cup cauliflower purée in 6 shallow warm bowls. Cover with breadcrumbs. Arrange the cauliflower florets over the breadcrumbs. Top with apple slices. Place 6–8 tarragon leaves over each dish and lastly drizzle the apple vinaigrette.
Recipe courtesy of Benjamin Sukle, chef and co-owner, birch, Providence