Make the pasta. Sift flour onto a dry work surface. Make a well in the center of flour and add rice, salt, oil and pureed squash. Mix gradually, kneading into a smooth, soft dough by drawing small amount of flour in from the edges as you knead. Add more flour if the dough seems too sticky or more water if it feels too dry--but in both cases, add small amounts very slowly so as not to jeopardize the quality of the dough. Continue kneading until dough is a soft, workable ball, about 10 minutes. Set aside. Makes about 1 pound of dough.
To make the gnocchi, flour a fork. Pinch off 1-inch pieces of dough and roll into balls between your fingers. Run the pasta ball on the fork to create ridges. Transfer to a parchment lined baking sheet that has been sprinkled with semolina. Repeat until you have made the desired amount of gnocchi. (The balance of the dough can be frozen.).
Bring a pot of water to the boil, with a pinch of salt and a drizzle of olive oil. Cook the gnocchi until just tender, about 2 minutes. The gnocchi will sink to the bottom of the pot. When it rises, it is done. Drain, but do not rinse.
While the pasta cooks, make the oil. Place all ingredients in a sauce pan over low heat and cook for 3-4 minutes to develop the flavors. Strain the oil and toss with cooked gnocchi. Garnish with fresh basil sprigs and serve immediately.