In a large mixing bowl, with an electric mixer on high speed, beat butter until creamy. Add sugars and beat well. Beat in egg yolks and vanilla extract.
In a separate bowl, sift together flour, baking soda, baking powder, and salt. Add to creamed mixture. Dough will be stiff.
Press dough flat onto a greased 10-by-14-inch baking sheet, cover with chocolate chips, and bake for 10 minutes.
Reduce oven heat to 325°F. Make meringue topping: Beat egg whites until very stiff; add brown sugar and beat well.
Spread meringue across top of dough (don't spread all the way to edges).
Return to oven for 12 to 15 minutes or until meringue is very light brown and dough is set.