Place the potatoes on a baking sheet, and toss with the olive oil, paprika, rosemary and salt.
Bake until tender when pierced with a fork, about 30 minutes, stirring halfway through.
Preheat the grill to medium-high heat. Alternatively, set a grill pan over medium-high heat.
Slice a strip lengthwise from zucchini to expose the inside of the vegetable. Discard or save for another use. Cut the 2 ends from the zucchini, and discard. Cut the zucchini lengthwise into ½-inch strips.
Lightly brush both sides of the zucchini pieces with olive oil, and sprinkle with paprika and salt.
Grill the zucchini until tender enough to roll, but not mushy, 2 to 3 minutes per side.
Spread 1 teaspoon of goat cheese on each zucchini slice. Place a potato at one end of each slice and top with the basil. Roll the potato up in the zucchini. Serve immediately.