In a large Dutch oven or heavy-bottomed pot, melt 6 Tbs of butter over medium heat.
Add the carrots, green onions, red onion, radishes, parsley, basil, and garlic.
Sauté, stirring often, for about 20 minutes until the vegetables soften and begin to color.
Cover the pot, reduce the heat to low, and let the vegetables simmer and sweat for an additional 15 minutes.
Uncover the pot and stir in the chopped tomatoes, zucchini, green bell pepper, white wine, salt, pepper, and sugar.
Bring to a simmer and cook, uncovered, for 45 minutes to 1 hour, allowing the sauce to reduce and the flavors to meld.
While the sauce simmers, prepare the cream base.
In a small saucepan, melt the remaining 1 Tbs of butter over low heat.
Whisk in the flour and cook for 2 minutes, stirring constantly, to create a roux. Slowly pour in the warm cream while whisking continuously to prevent lumps.
Add the tomato paste and whisk until the mixture is completely smooth.
Pour the creamy tomato mixture into the vegetable sauce.
Stir in the ½ cup of grated Parmesan cheese.
Continue to simmer the sauce over low heat, stirring occasionally, until it has thickened to your desired consistency.
Cook the conchiglie in a large pot of generously salted boiling water according to package directions until al dente.
Reserve about 1 cup (240 ml) of pasta water, then drain the pasta completely.
Pour the cooked pasta into a large, heated serving bowl. Ladle your desired amount of sauce over the shells, toss gently to coat, and serve immediately.
Garnish generously with additional grated Parmesan cheese.
Reserve a cup of the starchy pasta water before draining the noodles. If your sauce becomes too thick, you can stir in a splash of this liquid gold to thin it to the perfect consistency.
