Special equipment: Potato ricer or food mill and a gnocchi board
For the roasted tomato sauce: Preheat the broiler to high.
Put the tomatoes on a baking sheet and drizzle with 3 tablespoons of the olive oil. Season with salt and pepper and shake the baking sheet so the tomatoes roll around and get covered with oil. Place under the broiler until lightly charred and softened, 10 to 12 minutes.
While the tomatoes are roasting, heat a large skillet over medium heat. Add the remaining 3 tablespoons olive oil and the onions, season with salt and pepper and cook until translucent and softened, about 5 minutes. Add the red pepper flakes and garlic and cook for another minute. Stir in the roasted tomatoes and their juice, the white wine and tomato juice and let simmer for 2 minutes. Cover and cook on low until the tomatoes break down slightly and the flavors meld, 8 to 10 minutes. Add the parsley and basil and cook for another minute. Taste and adjust the seasoning if necessary. Keep warm.
For the gnocchi: Add the potatoes to a medium pot and fill with cold water. Add a very generous pinch of salt and bring to a boil over high heat. Cook until fork-tender, 10 to 12 minutes. Drain and return to the pot to let dry. Cool the potatoes until warm but not cold.
Press the potatoes through a ricer into a bowl. Add the egg and about 1/2 teaspoon salt. Add the all-purpose flour in 1/4-cup increments and gently knead with your hands to form a soft, smooth dough. Depending on the water content of the potatoes, you may not need to add all of the flour. If the dough is sticky, gently mix in more flour. The dough should be soft but not sticky. Do not over-work the dough; if you knead it too much it will get elastic and will make for chewy gnocchi. Roll the dough in a ball and cut into quarters.
On a floured work surface, roll out a quarter of the dough into a long rope about 1/2 inch in diameter. Slice the rope into 1-inch-long pieces. Dust a baking sheet with 1/4 cup of the semolina flour. Using a gnocchi board or the back of a fork, roll the gnocchi down the board to form ridges; these ridges will help the sauce stick to the gnocchi. Place onto the baking sheet. Repeat with the remaining dough. When all of the gnocchi have been rolled, dust the tops with the remaining 1/4 cup semolina flour. Shake the baking sheet so the gnocchi roll and get coated in the flour.
Bring a large pot of salted water to a boil.
Add the gnocchi to the boiling water and cook until they float, 3 to 5 minutes. Drain and return to the pot. Add half of the sauce and gently toss to coat. Transfer to a serving bowl and top with the remaining sauce. Serve immediately.