In a small saucepan over low heat, heat vanilla beans and olive oil very slowly until hot and vanilla is aromatic. Cool, strain, and store refrigerated.

Using either dental floss or a knife dipped in warm water, divide goat cheese log into 8 medallions. Carefully roll in chopped pecans to coat, pressing nuts into cheese so that they adhere. Set aside until ready to assemble the salads.

In a large bowl toss arugula with 3 ounces of the vanilla bean oil. Season with salt and pepper to taste and garnish each serving with one pecan-crusted goat cheese medallion