Place potatoes in a saucepan; cover with water. Bring to a boil. Reduce heat, and simmer 15 minutes or until tender. Drain potatoes in a colander over a bowl, reserving 1 1/2 cups liquid. Cool potatoes slightly, and cut into 1/2-inch pieces.
Heat 1 tablespoon oil in a small skillet over low heat. Add almonds, shallots, and garlic to pan; cook 8 minutes or until the almonds are golden, stirring often. Remove from heat; cool.
Place almond mixture in a food processor; add remaining 3 tablespoons oil, juice, cheese, harissa, and salt; process 1 minute or until well blended and almost smooth. With the processor on, slowly pour 1 1/2 cups reserved cooking liquid through food chute; process 1 minute or until smooth.
Combine pasta, potatoes, and almond mixture in a large bowl, tossing gently. Fold in arugula; sprinkle with basil.