Bring a large pot of water to a boil, salt it, add the pasta and cook it until al dente. Drain.
While the pasta is working, in a medium saucepan, melt 4 tbsp. butter over medium heat. Add the poblano, onion and garlic and cook until softened, 7 to 8 minutes. Whisk in the flour for 1 minute. Whisk in the chicken stock and simmer, stirring, for 5 minutes.
In a small saucepan, heat the creme fraiche (or crema) over medium heat. Whisk the warm cream into the poblano sauce. Transfer to a food processor or blender and puree until very smooth; season with salt.
In a large skillet, melt the remaining 2 tbsp. butter over medium-high heat. Add the shrimp and cook until firm and pink; season with salt and pepper. Add the pasta and poblano sauce to the shrimp; toss well. Sprinkle the thyme on top. Pass the cheese at the table, if desired.