Cook the pasta in boiling salted water until almost done, about 8 minutes.
Add the carrots and peas to the pot and continue cooking until the pasta and carrots are firm-tender, about 2 minutes.
Transfer the pasta, carrots, and peas to a large bowl. Add the bell pepper.
Whisk together the oil, vinegar, shallot, thyme, and salt and pepper to taste. Drizzle over the pasta; toss with the capers and tuna.
Divide among 4 bowls. Shave or grate Parmesan over the top.