Combine butter, sugar, lime juice and lime zest in 2-quart saucepan. Cook over medium heat, stirring occasionally, 2-4 minutes or until mixture just comes to a boil and butter is melted.
Beat eggs in bowl with whisk. Stir small amount of hot lime mixture into eggs. Whisk egg mixture into remaining hot lime mixture. Reduce heat to medium-low. Cook, stirring constantly, 4-6 minutes or until mixture reaches 160°F and is thick enough to coat back of metal spoon. Remove from heat. Stir in vanilla. Refrigerate about 2 hours or until completely cooled.
Beat whipping cream in bowl at high speed, scraping bowl often, until stiff peaks form. Gently stir into cooled lime mixture.
Assemble parfaits by breaking cookies in half. Place 2 cookie halves each in bottom of 6 parfait or serving glasses. Top with about 3 heaping tablespoons lime mixture and about 2 heaping tablespoons strawberries. Repeat layers two more times. Garnish each with 1 cookie half, if desired.
Variation: Strawberry Lemon Mousse Parfait: Substitute lemon juice and lemon zest for lime juice and lime zest.
Lime mixture can be made up to 1 day ahead. Store refrigerated in container with tight-fitting lid until serving time.