Preheat oven to 375°. Heat 2 Tbsp. extra-virgin olive oil in a large skillet over medium-high. Add 12 oz. cabbage, thinly sliced, and season with kosher salt. Cook, stirring occasionally, until slightly softened and starting to brown around the edges, about 4 minutes. Add 1 leek, white and pale green parts only, thinly sliced, season with more salt, and cook, stirring occasionally, until softened, 6–8 minutes.
Add 2 Tbsp. unsalted butter and 1 Tbsp. caraway seeds to pan and cook, stirring until butter is melted, about 1 minute. Add 2 Tbsp. apple cider vinegar and cook, scraping up any browned bits from bottom of pan, about 1 minute. Remove cabbage mixture from heat.
Whisk 7 large eggs and ⅔ cup sour cream in a large bowl to combine and season with salt and freshly ground pepper.
Scrape cabbage mixture evenly into 1 store-bought frozen pie shell, thawed, then pour egg mixture over. Bake quiche until filling is set and golden brown in spots and crust is golden brown all over, 30–35 minutes.
Toss 2 apples, thinly sliced, and 1 bunch radishes, trimmed, thinly sliced, in a medium bowl. Drizzle in remaining 2 Tbsp. apple cider vinegar and 1 Tbsp. extra-virgin olive oil, season with salt and pepper, and toss to coat.
Just before serving, add coarsely chopped dill to apple and radish salad and toss just to combine. Cut quiche into wedges and serve with salad alongside.