Cook the pasta according to the package directions, adding the pasta and peas at the same time. While the pasta and peas are cooking, make an ice water bath: Dissolve the 1 tablespoon kosher salt in 1/2 cup warm water in a large bowl. Add 4 cups each ice and water and reserve. Drain the pasta, cool in the ice water bath for 2 minutes, then drain again. Transfer to a bowl and toss with the olive oil, lemon juice and zest, cheese, salt, pepper, mint, and tarragon. Divide among bowls and garnish with additional mint and tarragon.