Line 2 heavy baking sheets with parchment paper. Finely chop the oats in a food processor. Transfer the oats to a medium bowl. Mix in the flour, baking powder, baking soda, and salt. Set aside.
Using an electric mixer, beat the butter and sugars in a large bowl until fluffy. Beat in the eggs and vanilla. Add the flour mixture and stir just until blended. Stir in the toffee, hazelnuts, and chocolate chips.
For each cookie, drop 1 rounded tablespoonful of dough onto sheet, spacing 1 inch apart (do not flatten dough). Bake until the cookies are golden (cookies will flatten slightly), about 15 minutes. Cool the cookies on the baking sheets for 5 minutes. Transfer to a cooling rack and cool completely. (The cookies can be prepared 1 day ahead. Store in an airtight container at room temperature.)