Bring a pot of salted water to a boil, add pasta and cook until al dente. Drain.
In a saucepan, melt 4 tablespoons butter. Add Poblano, onion and garlic and cook until softened. Whisk in flour for 1 minute. Whisk in stock and simmer.
In a saucepan, heat crema. Whisk warm cream into Poblano sauce. Transfer to a food processor or blender and puree until smooth, season with salt.
In a skillet, melt remaining butter. Add shrimp and cook until firm and pink, season with salt and pepper. Add pasta and Poblano sauce to shrimp, toss well. Sprinkle thyme on top.
Serve with cheese at the table.