Preheat the oven to 425 degrees F. Heat 2 tablespoons olive oil in a large ovenproof skillet over medium heat. Add the onion and cook, stirring occasionally, until softened, about 3 minutes. Add the garlic, chopped thyme, 1 teaspoon salt, and pepper to taste and continue cooking, stirring occasionally, until the garlic and onion are slightly golden, about 5 minutes. Add the wine and cook until mostly evaporated, about 2 minutes.
Meanwhile, combine the breadcrumbs or matzo meal, parsley, chives, the remaining 1 tablespoon olive oil, and salt and pepper to taste in a bowl; reserve 2 tablespoons for topping.
Arrange one-third of the potatoes over the onion in the skillet. Sprinkle with half of the remaining crumb mixture; top with another layer of potatoes. Repeat with another layer of the crumb mixture and potatoes. Pour the broth on top. Cover, bring to a boil and cook, undisturbed, 5 minutes.
Uncover, sprinkle with the reserved crumb mixture, drizzle with olive oil and season with salt. Transfer the skillet to the oven; bake until the potatoes are golden brown and crisp on top, about 45 minutes. Let rest 5 to 10 minutes before serving.