Rinse and core tomatoes; cut in half lengthwise, rub lightly all over with olive oil, and lay cut side up in a single layer in a 10- by 15-inch pan.
Bake tomatoes in a 450° regular or convection oven until edges begin to brown, 25 to 35 minutes.
Meanwhile, rinse, stem, and seed poblano chilies; cut lengthwise into 1/16- to 1/8-inch-wide strips. Peel and chop onion. In a 5- to 6-quart pan, combine chilies, onion, and 1 tablespoon olive oil. Stir often over medium-high heat until chilies are limp and beginning to brown, 10 to 15 minutes.
When tomatoes are done, push to 1 side of the pan. Scrape chili mixture into empty section; keep warm in a 150° oven.
In the 5- to 6-quart pan, bring 3 quarts water to a boil over high heat; add pasta. When boil resumes, reduce heat and boil gently until pasta is tender to bite, 6 to 10 minutes.
Drain pasta and return to pan. Set over high heat and immediately add 1 cup broth and the whipping cream; stir until boiling. For moister pasta, add more broth as desired (it soaks in quickly). Remove from heat and stir in chili mixture. Add 1/4 cup cheese, and mix. Pour pasta mixture into a wide serving bowl, sprinkle with 1/4 cup cheese, and arrange roasted tomatoes on top. Spoon onto plates. Add more cheese, salt, and pepper to taste. Accompany with baked bacon.