Preheat oven to 425°F and line a sheet tray with parchment paper or aluminum foil, if desired, for easier cleanup.
Using a food processor, process pretzels until finely ground; transfer to shallow dish. Spread flour in second shallow dish. Beat eggs and 2 tablespoons mustard in third shallow dish. In a separate mixing bowl, whisk remaining ⅓ cup mustard with honey and set aside.
Pat chicken dry and season with salt and pepper. Using tongs, dredge a chicken thigh in flour, dip in egg mixture, then coat with pretzel crumbs and press gently to adhere. Transfer chicken to one side of the sheet pan. Repeat with remaining chicken thighs.
Toss potatoes in mixing bowl with mustard and honey just enough to coat them and season with salt and pepper. Transfer to other side of the baking sheet and reserve the bowl. Drizzle both the chicken and potatoes liberally with olive oil. Transfer to oven and cook for 15 minutes.
Meanwhile, add the green beans and tomatoes to the same bowl you tossed the potatoes in. Drizzle with olive oil, season with salt and pepper and toss to coat.
Remove sheet pan from the oven and add the green beans and tomatoes to the open space on the pan (some overlap is fine). Return to the oven and cook for another 10 minutes until chicken has cooked through (165°F) and potatoes and veggies are fork tender.
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