Cook pasta according to package instructions, omitting salt and fat.
While pasta cooks, combine zest and juice of 1 lemon and 2 teaspoons olive oil in a large bowl; stir well with a whisk. Add artichoke hearts, cheese, bell pepper, and parsley; toss to combine.
Place peas in a colander; when pasta is cooked, drain pasta over peas. Shake well to drain, but do not run under cold water. Add pasta and peas to artichoke mixture, and toss well until thoroughly combined. Serve warm or at room temperature.