This classic chilled Spanish soup is like a super-smooth gazpacho.
Cut off a 4-inch piece from the baguette. Tear into bite-size pieces (you should have about 2 cups); transfer to a blender. Add 1/2 cup water to the blender and let stand until the bread softens, about 10 minutes.
Add the tomatoes, vinegar and garlic; pulse to blend. With the machine running, gradually add 1/2 cup EVOO and process until very smooth, about 3 minutes; season with salt and pepper. Cover and chill until cold, about 4 hours. Thin with cold water if too thick.
Preheat the oven to 400°. Slice the remaining bread on a sharp angle; arrange on a baking sheet and bake until toasted, about 13 minutes. Drizzle with EVOO. Divide the soup among bowls; top with the hard-boiled eggs and ham. Drizzle with EVOO. Serve with the toasts.
