Position racks in upper and lower third of oven; preheat to 425 degrees F.

Toss potatoes and sweet potatoes with 2 tablespoons oil, 1/2 teaspoon salt, 1/4 teaspoon pepper and garlic powder in a large bowl until well coated. Divide between 2 large baking sheets and spread in an even layer. Roast, rotating the pans from top to bottom about halfway through, until tender and beginning to brown, 20 to 25 minutes.

Meanwhile, heat the remaining 2 tablespoons oil in a large saucepan over medium heat. Add onion; cook, stirring frequently, until very soft and golden brown, 5 to 8 minutes. Add flour and the remaining 1/2 teaspoon salt and 1/4 teaspoon pepper; cook, stirring for 1 minute more. Add almond milk; cook, stirring and scraping up any brown bits at the bottom of the pan. Increase heat to medium-high; cook, stirring, until the sauce thickens and bubbles, about 3 minutes. Remove from heat.

When the potatoes are done, remove them from the oven. Preheat the broiler. Transfer half the potatoes to a 2-quart broiler-safe baking dish. Spread half the sauce over the potatoes. Add the remaining potatoes and top with the remaining sauce, paprika and almonds. Broil, watching carefully, until the sauce is bubbling and the almonds are beginning to brown, 1 to 5 minutes, depending on your broiler. Let stand 10 minutes. Serve topped with thyme.