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Arrange oven racks evenly spaced in upper and lower thirds of the oven. Set one sheet pan in the oven to preheat it. Preheat oven to 425 degrees F.
Toss potatoes with 1 tablespoon oil, ½ teaspoon salt and pepper. Spread the potatoes on another (room temperature) baking sheet and transfer to the oven and set a timer for 35 minutes.
Stir 1 tablespoon oil, garlic, paprika, ¾ teaspoon salt and pepper to taste in a small bowl. Brush over the pork chops. Toss the green beans with the remaining 2 teaspoons oil and remaining ¼ teaspoon salt and pepper to taste in a large bowl.
When the timer has 20 minutes remaining, remove the pre-heated pan from the oven and spread the green beans on one side and the pork chops on the other. Immediately transfer to the oven. Roast until an instant read thermometer inserted into the thickest part of the pork, near the bone registers 145 degrees, 16 to 19 minutes.
Meanwhile, bring raspberries, honey, shallot, vinegar and ½ teaspoon salt to a simmer in a saucepan over medium high heat, stirring often. Reduce heat and simmer until thick, 5 to 8 minutes. Strain out the seeds by pressing though a fine-mesh sieve and set aside.
Serve the pork chops, potatoes and green beans hot, drizzled with the raspberry sauce.