Heat oven to 450°F and arrange rack to the top of the oven. Lightly coat a baking sheet with oil and set aside.
Take a small spoon and scrape 3 tablespoons of adobo paste from the jar, trying to avoid as much oil as possible. Transfer to a large bowl and using the back of a spoon, smash adobo paste against the bottom of the bowl to smooth it out.
Add brown sugar, lime juice, and salt and whisk to combine.
Peel the potatoes and cut into 1/4-inch thick sticks. Toss with the adobo marinade and let sit 5 minutes.
Lift potatoes out of the bowl letting any excess marinade drip back into the bowl. Spread potatoes into a single layer on a baking sheet.
Bake until crisped and brown, about 15 minutes, turning halfway through.