ANCHOVY VINAIGRETTE: In a small skillet, heat oil over medium-high heat. Add anchovy paste and garlic, and cook, stirring, until anchovies dissolve and garlic is fragrant, 1 minute. Whisk in vinegar. Set aside to cool to room temperature.
SALAD: In a medium saucepan fitted with a lid, place a steamer basket over 1 inch of salted water. Bring water to a boil. Fill steamer basket with potatoes, cover, and reduce heat to medium-low. Steam potatoes until tender, 12 to 15 minutes.
Meanwhile, in a small saucepan fitted with a lid, place eggs and add enough water to cover by 1 inch. Bring water to a simmer over medium heat, about 12 minutes. Once water begins to bubble, remove saucepan from heat and cover. Let eggs stand in hot water 8 minutes, then place under cold running water until cool enough to handle. Remove shells, and cut eggs into quarters.
On a large serving platter, scatter tomatoes, pepper, manchego, cooked potatoes, and quartered eggs. Sprinkle with salt and pepper, and spoon dressing over the salad before serving.