Add 2 cups of pasta to a large pot. Fill water to about 2 inches over the pasta. Set to boil on medium-high heat.
Rinse the asparagus. Chop 1-2 inches off the ends. Chop asparagus into roughly 1-inch pieces. Rinse the snow peas. Chop off the ends if desired. Chop the poblano and shallots. Peel and press the garlic. If you don't have a garlic press, chop the garlic into tiny pieces.
We will be adding the snow peas and asparagus to the pot with the pasta once the pasta is almost cooked. The pasta should take about 15 minutes to cook, you can add the vegetables in after about 10-12 minutes. Once cooked, strain the pasta and vegetables and set aside.
Add 2 tablespoons of olive oil to a large skillet over medium heat. Add the chopped poblano first and let it saute for 2 minutes, stirring intermittently. Add the shallots next. Continue to stir intermittently. You don't want them to burn, just to caramelize a bit. Add the garlic last once the poblano and shallot are mostly cooked. You don't want the garlic to burn.
In the same saute pan, add the broth, coconut milk, spices and carrots. Add the cornstarch slurry. A cornstarch slurry is a 1:1 ratio of water to cornstarch. Mix everything together. It will start to thicken as it cooks. I like to stir intermittently to be sure nothing sticks to the bottom of the pan.
Add the pasta, asparagus, and snow peas. By now, the broth should be thickened. Mix everything together so the sauce is distributed all over the pasta and vegetables. I like to let everything cook together for about 5 minutes before serving.