In a large skillet combine squash and sweet potatoes. Pour 1 cup water over all. Bring mixture to boiling; reduce heat. Simmer, covered, about 8 minutes or until vegetables are tender. Drain mixture. Set aside.
In the same large skillet cook the sweet pepper, onion, and garlic in hot oil over medium heat for 5 minutes or until onion is tender, stirring occasionally. Stir in brown sugar until combined. Remove from heat. Stir in the 1 teaspoon thyme, the basil, salt, crushed red pepper, and black pepper.
Carefully stir in the potato mixture. Place spinach in salad bowl or on a platter. Top with warm potato salad. Sprinkle with additional snipped fresh thyme, if desired. (Or, let potato mixture stand at room temperature for up to 2 hours before serving over spinach.)