1. Arrange a rack in center of oven and preheat to 400°F. Coat a rimmed baking sheet with oil.
2. Pulse garlic in a food processor until finely chopped. Add celery, beans, and mushrooms and pulse until coarsely chopped. Transfer to a large bowl. Stir in egg, panko, and 3/4 tsp. salt. Using your hands, roll tablespoonfuls of bean mixture into balls. Transfer to prepared baking sheet, packing them snuggly. Roast veggie balls, turning halfway through, until firm and cooked through, 25–30 minutes.3.
3. Meanwhile, cook butter, hot sauce, and maple syrup in a small saucepan over medium heat until butter is melted. Stir until smooth; set aside.
4. Make dip: Whisk sour cream, buttermilk, blue cheese, pepper, 1 Tbsp. plus 2 tsp. chives, and remaining 1/4 tsp. salt in a medium bowl. Top with remaining 1 tsp. chives.
5. Transfer veggie balls to a large bowl. Toss with hot sauce mixture and serve with blue cheese dip alongside.
Veggie balls can be formed, not cooked, 1 day ahead; cover and chill.