Cream together butter, brown sugar and pudding mix until light and fluffy.
Add eggs and vanilla, mixing until combined.
Stir in flour and baking soda.
Add fruity pebbles and 1 cup of white chocolate chips, mixing until evenly dispersed.
Scoop rounded Tablespoons full (or use a medium cookie scoop) onto parchment lined or nonstick cookie sheets leaving at least 2 inches between cookies. Top each ball of dough with a couple of the reserved white chocolate chips.
Chill for at least 30 minutes.
Preheat the oven to 350°F. Bake cookies for 9-11 minutes.
Cool on the pan for 5 minutes and then remove to a wire rack to cool completely.
Store in an airtight container at room temperature for up to a week or freeze for up to 3 months.