Khao soi paste:

4 large dried New Mexico or guajillo chiles, stemmed, halved, seeded
2 medium shallots, halved
8 garlic cloves
1 2" piece ginger, peeled, sliced
1/4 cup chopped cilantro stems
1 tablespoon ground coriander
1 tablespoon ground turmeric
1 teaspoon curry powder

Soup:

2 tablespoons vegetable oil
2 14-ounce cans unsweetened coconut milk
2 cups low-sodium chicken broth
1 1/2 pounds skinless, boneless chicken thighs, halved lengthwise
1 pound Chinese egg noodles
3 tablespoons (or more) fish sauce (such as nam pla or nuoc nam)
1 tablespoon (packed) palm sugar or light brown sugar
Kosher salt
Sliced red onion, bean sprouts, cilantro sprigs, crispy fried onions or shallots, chili oil, and lime wedges (for serving)

Ingredient info: Dried chiles are available at Latin markets; Chinese egg noodles and chili oil are available at Asian markets. All can be found at many supermarkets.