Heat a drizzle of extra-virgin olive oil in a skillet over medium heat. Add the garlic and speck and cook for 2 minutes, stirring. Add the corn and cook until it's creamy and sweet, about 8 to 10 minutes. Add the butter and cream. Season with salt and pepper and stir in half the scallions.
Preheat the broiler, if using, and char the bread under the hot broiler or in an electric panini press. Top the toasts with the corn mixture and garnish with the remaining scallions.