Preheat oven to 350 degrees. In large mixing bowl, combine peanut butter, sugars, egg, and vanilla. Mix until cookie dough is formed.
Using a medium sized cookie scoop, place cookie dough balls onto ungreased cookie sheet, spacing about 2 inches apart. Flatten cookie with bottom of glass or measuring cup to approximately ½ inch thickness. Bake 10-12 minutes. Cookies will appear slightly underdone but will set up as they cool. Repeat with additional dough.
Allow cookies to cool on cookie sheet for at least 5 minutes before transferring to cooking rack. Cool completely before moving on to step 4.
Line cooled cookie sheet with parchment or waxed paper. In microwave safe bowl or pyrex measuring cup, add chocolate chips and vegetable oil and heat for 30 seconds, stir, then continue in 15 second intervals until completely melted and smooth.
Dip cookie into chocolate until ⅓ of it is coated. Scrape off excess chocolate from bottom of cookie and place on lined cookie sheet. Sprinkle with small amount of salt. Repeat with all cookies and chill until chocolate has hardened.