Scoop 1 tablespoon Nutella dollops onto parchment-lined plate (about 12). Freeze 30 minutes until firm.
In a large mixing bowl, beat butter, brown sugar, and granulated sugar with electric mixer on medium until fluffy (3 minutes).
Add egg and vanilla, mix until smooth. Whisk flour, baking soda, and salt in separate bowl. Add dry ingredients to wet in two batches, mixing just until combined. Fold in chocolate chips.
Cover dough and chill in fridge 30 minutes.
Preheat oven to 350°F. Line baking sheets with parchment paper.
Scoop 2 tablespoons dough, flatten in palm. Place frozen Nutella in center. Wrap dough around Nutella, seal edges completely. Roll into ball. Place on sheet, spacing 2 inches apart.
Bake 10 minutes until edges are golden and centers look soft. Cookies will firm up as they cool.
Let cool on baking sheet 5 minutes. Transfer to wire rack. Serve warm for gooey center.