Step 1

Place the potatoes, carrots, and olive oil in a large, deep nonstick skillet with a tight-fitting lid or a Dutch oven. Turn the heat to medium high, then sprinkle with 1/2 teaspoon salt and 1/4 teaspoon pepper and stir to coat. When the skillet becomes hot and begins to sizzle, immediately reduce the heat to low. Cover and cook until the vegetables soften and brown, about 25 to 35 minutes. Shake the pan occasionally to prevent the potatoes from sticking. Remove the pan from the heat and let sit for 5 minutes, covered. Remove the vegetables to a dish or plate and set aside.

Step 2

Return the skillet to medium-low heat. Add the sausage pieces and cook, stirring occasionally, until the sausage has begun to brown and is almost (but not completely) cooked through, about 12 minutes. To the skillet, add the quartered mushrooms, remaining 1/2 teaspoon salt, 1/4 teaspoon pepper, and oregano. Cook for 3 minutes, then add the garlic, half of the green onions, and the cherry tomatoes. Continue cooking until the mushrooms become slightly brown and the tomatoes soften and lose their firm shape, about 5 additional minutes. Check the sausage for doneness. If not yet ready, cook a few minutes longer, until cooked through.

Step 3

Add the reserved potatoes and carrots to the skillet and mix well. Stir in the peas, then cook 2 to 3 additional minutes to warm through. Sprinkle with remaining green onions, then serve.