Weigh or lightly spoon flour into dry measuring cups; level with a knife. Combine flour, cocoa, and salt in a bowl, stirring with a whisk.
Place sugar, butter, and oil in a bowl; beat with a mixer at medium speed until well combined (about 5 minutes). Add eggs, 1 at a time, beating well after each addition. Add vanilla; beat 1 minute. Add flour mixture to butter mixture, beating at low speed just until combined. Add chocolate; beat at low speed just until combined. Cover with plastic wrap; chill 30 minutes.
Preheat oven to 350°.
Drop dough by 1 1/2 tablespoonfuls 2 inches apart onto baking sheets lined with parchment paper. Bake at 350° for 8 minutes or until almost set. Cool on pan 2 minutes or until firm. Remove cookies from pan; cool on wire racks.