Coat a 12-cup bowl with nonstick spray; line with plastic wrap, extending wrap over sides by at least the width of the bowl. Have rimmed baking sheet ready.
Cut carton off chocolate peanut butter ice cream. Cut ice cream in 3/4 inch thick rounds. Place slices in bowl to cover bottom and side up to 1 inch from top, cutting slices to fit. With a spatula, fill gaps. Freeze twenty minutes, or until form. Meanwhile, refrigerate dulce de leche ice cream to soften slightly.
Cut candy bars in 1/4 inch thick slices (total 1 cup). Use a potato masher or large spoon to stir ice cream to soften evenly; stir in candy. Spoon ice cream into bowl; spread level. Sprinkle crushed cookie crumbs over top; press into ice cream. Fold plastic wrap over ice cream to cover. Freeze overnight, or up to 2 weeks.
Up to one day ahead: Cut cardboard or a paper plate to fit on crumbs. Invert bombe and cardboard together onto a wire rack over a rimmed baking sheet. Remove bowl and plastic wrap. Quickly smooth any wrinkles. If ice cream starts to melt, refreeze before coating. Pour most of shell coating over bombe, using spatula to spread evenly to coat. Garnish with a drizzle of remaining coating. Transfer to serving plate. Freeze until serving.