Preheat the oven to 375 degrees F (190 degrees C).
Peel off outer layers of the garlic but leave cloves intact. Chop about 1/2 inch off the top of the garlic head and place in a ramekin or small casserole dish. Drizzle the exposed side with 2 tablespoon olive oil and sprinkle with 1/4 teaspoon salt. Cover with aluminum foil.
Roast in the preheated oven until tender, 45 minutes to 1 hour. Remove from the oven and cool for 15 minutes. Remove roasted garlic by squeezing it from the skins; set aside.
Heat remaining 1/4 cup olive oil in a deep skillet over medium-high heat. Add onion, cayenne, and remaining 1 teaspoon salt. Reduce heat to medium and cook until onion is translucent and slightly golden, about 5 minutes.
Add tomatoes and white wine and continue to cook until most of the wine has been reduced, about 5 minutes. Add butter and cook until completely melted, 1 to 2 minutes.
Add roasted garlic and enough chicken broth to completely cover the tomatoes; bring to a boil. Reduce heat to a simmer and cook until sauce has reduced and thickened, about 15 minutes.