Preheat oven to 350 degrees. Spread almonds in a shallow pan; bake until lightly toasted and fragrant, 5 to 7 minutes, shaking pan halfway through. Remove to a bowl to cool, then chop finely.

Line a 15-by-10-inch baking sheet with foil; mist with cooking spray. Arrange crackers in a single layer on sheet, breaking crackers as necessary to fit.

Bring butter and sugar to a boil in a small pan over medium-high heat, stirring occasionally. Boil for 3 minutes, stirring constantly. Remove from heat; stir in vanilla. Spread mixture evenly over crackers. Bake for 13 minutes. Remove sheet from oven; add peanut butter in dollops. Return to oven until peanut butter begins to melt, 1 to 2 minutes. Transfer sheet to a wire rack.

Spread peanut butter evenly. Sprinkle both types of chocolate chips over; let stand until chips soften, about 1 minute. Spread chips over peanut butter. Sprinkle with almonds. Let stand for 30 minutes. Place sheet in refrigerator; chill until chocolate is firm, about 30 minutes. Break into approximately 20 pieces. Refrigerate in an airtight container for up to 1 week.