Preheat the oven to 400°F.
Arrange the cabbage wedges on a baking sheet and drizzle with one and one-half tablespoons of olive oil, then sprinkle with salt and pepper.
Place the peeled peach wedges on a separate baking sheet and drizzle with one tablespoon of olive oil, then sprinkle with salt and pepper.
Roast the cabbage for 20 to 25 minutes, flipping halfway through, until the edges are browned and crisp.
After the cabbage has roasted for 10 minutes, add the peaches to the oven and roast for about 15 minutes until lightly caramelized.
Remove the cabbage from the oven, let it cool for a few minutes, then cut it into bite-size chunks.
Warm the remaining one-half tablespoon of olive oil in a large soup pot over medium heat.
Add the diced onion and cook for about 5 minutes, stirring occasionally, until softened.
Add the minced garlic and cook for 1 more minute, stirring often.
Pour in the vegetable broth.
Add the chopped roasted cabbage, roasted peach wedges, and fresh sage leaves.
Season with the teaspoon of kosher salt and the half teaspoon of black pepper.
Simmer gently over medium-low heat for 15 minutes to allow the flavors to blend.
Taste the soup and adjust seasoning.
If the flavor needs brightening, stir in the tablespoon of apple cider vinegar.
Ladle the soup into bowls and serve warm.