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