Preheat the oven to 350°F. Line 2 cookie sheets with parchment paper.
In the bowl of a stand mixer fitted with the paddle attachment, add the butter, cane sugar, and vanilla extract. Mix on low until combined, then set a timer for 5 minutes and mix until the mixture is light in color and fluffy.
Add the egg and flour, and mix on low until combined into a smooth dough.
Using your hands, form the dough into 24 balls and place them on the prepared baking sheets, and flatten them slightly so they are about 2-inches in diameter.
Using your thumb, give a gentle press into the middle of the cookie to create indentations in each cookie.
Bake for 20 to 22 minutes, or until lightly browned on the bottom.
While the cookies are baking, open the chocolate eggs so they are ready. Melt the white chocolate using a double boiler. Or, alternatively, in a microwave safe bowl for 30 second intervals, stirring between each one.
Divide the white chocolate into two bowls, add a little bit of the pink dye into one bowl and mix together.
When the cookies come out of the oven, press a chocolate egg into the center of each cookie.
Drizzle the white chocolate on top of the eggs after they are pressed in. You can leave them as a drizzle, or using a chopstick, swirl the two chocolates together. Top with rainbow sprinkles. You can add toppings to some of the eggs or leave them all plain, totally up to you!
Store in a cool dry place for up to 3 days.