Cook the pasta according to directions in a large pot of water. When the pasta is al dente, scoop the pasta out with a mesh strainer, leaving the boiling water in the pot and put the pasta into a large bowl. Set aside.
Peel and cut the carrots into large chunks. Put the carrots and garlic cloves into the boiling water.
Boil, reducing heat as needed, until the carrots are very tender. About 10-15 minutes.
Drain the carrots and garlic, getting rid of the cooking water at this point.
Add the carrots, garlic, red curry paste(using 1 TBSP if you want it less spicy and 2 TBSP if you want more spice), coconut milk and a pinch of salt and pepper to a blender.
Blend, scraping down the sides as needed, until the sauce is completely smooth.
Now, using the pot you were using to cook everything in, heat the oil on medium high.
Add the shallot and ginger to the pot. Sauté, reducing heat as needed, until the shallot is translucent. About 2-3 minutes.
Pour the sauce you made into the pot and stir to combine everything.
Bring to a simmer, reduce heat to low, and simmer for 1-2 minutes.
Taste and adjust seasonings. Adding more salt and pepper if needed.
Pour the cooked pasta into the pot and toss with the sauce. Let the pasta heat back up for about 3-5 minutes, since it has been sitting for a bit.
Serve immediately with chives and sautéed greens if desired.