In a 5- to 6-quart pan over high heat, bring 3 quarts water to a boil. Add spaghetti and cook, stirring occasionally, until tender to bite, 10 to 12 minutes.
Drain pasta and immerse in cold water; when cool enough to touch, in about 1 minute, drain again. Mix with butter.
Lift pasta, a handful at a time, and let strands shake out until fairly straight; lay neatly around the center of a ring mold (see notes). Repeat, using all the pasta; pat to make level. Let stand at least 1 hour (see notes).
Invert a flat, rimmed microwave-safe plate over mold. Holding containers together, flip over and lift off mold.
Cover pasta with microwave-safe plastic wrap. Heat in a microwave oven on full power (100%) until pasta is hot, about 5 minutes. Uncover and fill with beef stroganoff.