In a small saucepan, melt entire stick of butter. Set aside and cool to room temperature. In a stand mixer or with a hand mixer, whisk eggs, 1/3 cup sugar and vanilla on medium speed until they double in size and turn light yellow, about 8 to 10 minutes.
In a medium bowl, sift the salt, 1/3 cup sugar and flour together. Gradually fold the flour into the egg mixture one-third at a time. Pour the cooled, melted butter into the batter and gently combine. batter and gently combine.
Coat a madeleine mold with cooking spray. Gently pour batter into each cookie mold up to the edge. Place in the oven for 14 to 17 minutes or until golden brown. Remove from oven. Using a butter knife, gently loosen cookies around the edges. Place a cooling rack over the top and turn cookie pan upside down, revealing the signature scalloped tops of the madeleines.
In a microwave-safe bowl, add hazelnut spread and microwave 30 seconds at a time until thin and smooth. Add coconut oil to thin out. Dip baked madeleines halfway in hazelnut topping. Garnish with toasted hazelnuts and a pinch of sea salt. Enjoy!