Parboil the potatoes. Put 1 1/2 pounds of cubed red or Yukon Gold potatoes in a large pot. Cover with cold water by about 1 inch and stir in 1 tablespoon salt and 1/2 teaspoon baking soda. Bring to a boil over high heat, then reduce to medium and simmer for about 5 minutes, until a fork just pierces a cube and the center still feels slightly firm.
Heat the oven. While the potatoes cook, set a rack in the middle of the oven and preheat to 425°F. Lightly oil a large rimmed baking sheet.
Make the spice mix. In a small bowl, stir together 1 teaspoon cornstarch, 1 teaspoon chili powder, 1 teaspoon garlic powder, 1 teaspoon onion powder, 1 teaspoon ground cumin, 1/2 teaspoon dried thyme, 1/2 teaspoon salt, 1/2 teaspoon freshly ground black pepper, and 1/4 teaspoon cayenne pepper, if using.
Let the potatoes steam-dry. Drain them in a colander and give it a few shakes to rough up the edges. Spread the cubes on a paper towel-lined tray and let them steam-dry for 10–15 minutes.
Season the potatoes. In a large bowl, toss the potato cubes with 3 tablespoons olive oil or canola oil, then add the spice mix and toss until evenly coated.
Roast in a single layer. Spread the potatoes on the prepared baking sheet with a little space between the cubes. Roast for about 30 minutes, until golden brown and crisp.
Top and serve. Taste for salt and serve hot, or finish with 1/2 cup crumbled queso fresco and your choice of sour cream, salsa verde or pico de gallo, chopped cilantro, and a squeeze of lime. Add diced green chiles, sliced green onions, or a fried egg if you like.
