Mince garlic. Cut sweet potatoes into 1/2" thick fries. Zest and halve lime. Quarter one half and juice remaining half. Stem jalapeño, halve, seed, and mince. Keep seeds if you prefer more spice. Stem cilantro, mince stems, and coarsely chop leaves. Rinse chicken breasts and pat dry.

Combine white wine vinegar (reserve 1 tsp. for dipping sauce), cumin, paprika, half the garlic (reserve remaining for dipping sauce), 3 Tbsp. olive oil, 1 tsp. salt, and 1/2 tsp. pepper in a medium mixing bowl. Add chicken and mix to coat completely. Marinate 10 minutes.

Place sweet potato fries on one side of prepared baking sheet. Toss with 1/2 tsp. olive oil, 1/2 tsp. salt, and 1/4 tsp. pepper. Spread into a single layer, roast 10 minutes, and remove from oven.

Flip potatoes and place chicken on other half of baking sheet. Sprinkle each chicken breast with 1/4 tsp. salt. Bake 20 minutes, or until sweet potatoes are tender and lightly browned and chicken reaches a minimum internal temperature of 165 degrees. Remove baking sheet from oven and turn on broiler. Broil 1-3 minutes, or until edges of both chicken and potatoes are lightly charred. Let chicken rest 3 minutes. Broiler heat varies, so keep an eye on chicken and potatoes to avoid burning!

Add mayonnaise, sour cream, cilantro (reserve a pinch for garnish), 1 Tbsp. lime juice, lime zest, reserved white wine vinegar, remaining garlic, jalapeño pepper (to taste) and 1/2 tsp. olive oil to a small bowl. Season with a pinch of salt and pepper. Stir to combine and set aside.

Pile fries on a plate. Slice chicken breast into 1/4" pieces and place on plate next to fries. Serve dipping sauce on side. Garnish with lime quarters and remaining cilantro.