Preheat the oven to 400 degrees. Lightly spray a sided sheet pan with nonstick cooking spray.
To prepare the shrimp: Place shrimp in a large bowl and add enough water to cover shrimp by at least 1 inch. Sprinkle with 2 tablespoons salt and sugar, and swish it around in the water so it dissolves. Set aside, while you prepare the other ingredients.
To prepare the seasoning: Mix together 1 garlic clove, 1 tablespoon salt, cayenne pepper, paprika and 2 tablespoons oil. Taste and adjust seasoning as needed. It should have a mild spiciness to it, but not overpowering.
To prepare the vegetables: In a medium bowl, whisk together 2 tablespoons olive oil, Dijon, 1 garlic clove, a few pinches of salt and pepper, seasoning blend and oregano. The mixture should look emulsified, not separated or grainy. Add the quartered potatoes and toss to coat. Place the coated potatoes on one side of the sheet pan and place in the oven for about 20 minutes.
To cook shrimp and vegetables: Drain and rinse the shrimp. Pat the shrimp dry and sprinkle with the seasoning mixture. Place the frozen beans in the same bowl that held the potatoes and toss to coat with any remaining Dijon mixture.