Place egg whites in a large bowl. Let stand at room temperature for 30 minutes. Preheat oven to 300 degrees F. Line two very large baking sheets with parchment paper or foil. Draw an 8-inch circle on one sheet of paper or foil. Draw two 8-inch circles on other sheet of paper or foil, leaving about 1 inch between circles. Set aside.
Add vanilla and cream of tartar to egg whites. Beat with an electric mixer on medium speed until soft peaks form (tips curl). Gradually add the 1-1/3 cups sugar, 1 tablespoon at a time, beating on high speed about 5 minutes or until stiff peaks form (tips stand straight) and sugar is nearly dissolved. Gently fold in the 1 cup pistachio nuts.
Spread meringue over circles on paper or foil. Bake all of the meringues at the same time on separate oven racks for 35 minutes. Turn off oven; let meringues dry in oven with door closed for 1 hour.
Meanwhile, in a medium bowl, combine cream cheese and butter. Beat on medium speed until smooth. Beat in the 1/3 cup sugar. Add whipping cream; beat on low speed until combined, then on medium speed just until soft peaks form (tips curl). Cover and chill until needed.
Before assembling, place banana slices in a small bowl. Drizzle with lime juice; toss gently to coat. To assemble, lift meringues off paper or foil. Place one meringue on a serving plate. Spread with one-third of the whipped cream mixture. Top with one-third of the banana slices and 1 rounded tablespoon of the pistachio nuts. Repeat layers two more times. Cover loosely and chill for 1 to 2 hours. Before serving, drizzle with honey. Makes 12 servings.