Combine the peanut butter, tamari, honey, lime juice, and chili garlic sauce in a small saucepan and heat, stirring, over medium heat until it is smooth and fully combined. Set aside.
Bring a large pot of water to a boil and cook the noodles per the package directions. Drain, rinse with cold water, and set aside.
Heat a large skillet over medium-high heat. Add the pork and break up with a spatula; let cook until it starts to get browned, 3-5 minutes. Remove any excess grease from the pan.
Reduce heat to medium-low, add the carrots, peanut sauce, and 1½ cups of broth. Stir to combine. Add the cooked noodles and toss with tongs until fully coated; you may need to add more chicken broth to thin out the sauce. Add the spinach and 2 green onions and cook, tossing with tongs, until the spinach has wilted, and the noodles are fully coated with sauce.
Divide the noodles among 4 shallow bowls and top with the remaining green onion and chopped peanuts. Serve more chili garlic sauce on the side, if desired.