1. In a medium saucepan, cover the beets with water and bring to a boil. Simmer over moderate heat until tender, about 25 minutes. Transfer the beets to a plate and let cool, then peel and cut into 1/2-inch dice. Reserve 2 cups of the cooking liquid in the saucepan.
2. Add the maple syrup to the pan and boil over moderately high heat for 5 minutes. Stir in the beets and cayenne and simmer over moderate heat until the beets are sweet and hot, about 30 minutes. Using a slotted spoon, transfer the beets to a plate. Boil the cooking liquid until slightly thickened, about 8 minutes. Return the beets to the pan and let cool to room temperature.
3. In a small bowl, whisk 2 tablespoons of the beet syrup with the vinegar, olive oil and garlic and season with salt. Spread each toast with 2 teaspoons of goat cheese; sprinkle with poppy seeds.
4. In a large bowl, toss the lettuce with the beets and vinaigrette. Mound the salad on plates, set the goat cheese toasts alongside and serve.
Make Ahead: The recipe can be prepared up to 1 day ahead through Step 2 and refrigerated.