Step 1Bring a large pot of salted water to a boil. Add the noodles and cook for 3 minutes. Drain, rinse under cold water until cold and drain again.
Step 2Meanwhile, heat a Dutch oven or other wide, large pot over medium-high heat. Open the can of coconut milk and scoop 2 to 3 spoonfuls of the solid fat into the Dutch oven. Add half of the shallots, season with salt, and cook, stirring occasionally, until tender, 3 to 4 minutes.
Step 3Add the curry paste and cook, stirring, until a shade darker and toasty, 1 to 2 minutes. Add everything remaining in the can of coconut milk, then fill the can with water and pour it in. Bring to a boil over high heat, then reduce the heat to simmer. Taste and add more curry paste and salt if you’d like. Simmer for 10 minutes.
Step 4While the sauce simmers, run a vegetable peeler along the lengths of the carrots to create ribbons. You’ll have a flat core of carrot remaining; you can snack on it or save for another use.
Step 5Add the noodles and carrots and stir until both are just tender with a little bite, about 1 minute. Divide among serving bowls and serve immediately.