Position oven racks in the top and bottom thirds of the oven and preheat to 375 degrees F. Line 2 baking sheets with parchment.
Whisk together the flour, baking soda, salt and baking powder in a medium bowl. In a stand mixer or large bowl using a hand mixer, cream the butter for 1 minute. Add the sugar and cream for an additional 3 minutes. Beat in the vanilla and egg. Gradually beat in the dry ingredients until uniform, then add enough of the half-and-half (about 2 tablespoons) to moisten the dough and make it soft (but not wet). Fold in the sprinkles and 2/3 cup of the white chocolate chips.
Roll rounded teaspoons of dough into 24 balls and put on the prepared baking sheets. Chill the remaining dough in the refrigerator. Dip your fingertips into the remaining half-and-half and use them to slightly flatten the top of each cookie.
Bake until the cookies are set on top and light golden brown around the edges, about 15 minutes. Transfer the cookies to a wire rack to cool completely. Allow the baking sheets to cool, then line them with new parchment and repeat the forming and baking process with the remaining dough.
Once the cookies are all baked and cooled, put the remaining 1 cup white chocolate chips in a small heatsafe bowl and microwave on high, stirring halfway through, until just melted, about 1 minute. Use a spoon to drizzle the chocolate over the cookies. Allow the chocolate to set before serving, about 30 minutes. Store in an airtight container at room temperature for up to 1 week.