Preheat oven to 350° F / 175° C. Line two baking sheets with silicone baking mats or parchment, and set aside until ready to use.

In a mixing bowl, combine flour, sugar, baking powder, and salt.

Add cubed butter to flour mixture and use your hands to combine. The mixture will resemble breadcrumbs.

Add 3 eggs and vanilla extract to the flour-butter mixture, followed by chocolate chips and 4 tablespoons rainbow nonpareils. Knead by hand until a soft dough forms.

Lightly flour countertop. Divide dough into two equal portions, and roll each portion into a log. Each log should measure approximately 8 inches (20 centimeters) long and about  3 inches (8 centimeters) wide.

Place two logs on baking sheet, making sure to allow a good amount of space between the two. Use a pastry brush to brush the tops of the logs with egg white.

Sprinkle the tops of each log with a generous helping of rainbow nonpareils, using your hands to gently pat the sprinkles into the dough.

Bake in preheated oven for 25 minutes. Remove from oven and cool for 10 minutes on tray.

Using a serrated knife, cut each log on the diagonal, creating 1-inch / 2.5-centimeter wide slices. Place slices upright on baking sheets and bake for an additional 15 minutes.

Transfer biscotti to a wire rack and cool completely prior to serving.

Chocolate chip rainbow biscotti are best enjoyed within 1-2 days of baking, but may be stored in an airtight container at room temperature for up to 5 days. Biscotti can also be frozen, and will thaw quickly at room temperature.