Preheat the oven to 400°F/200°C. Place the cherry tomatoes in a large, shallow roasting pan and spread them out so they are in a single layer. Slice or chop the garlic and toss with the tomatoes. Drizzle over the olive oil and balsamic vinegar and lightly toss the tomatoes to coat. Season with kosher salt and pepper. Bake for 35 to 40 minutes or until the tomatoes start to darken and are very soft.
Meanwhile bring a large pot of water to a boil and season generously with kosher salt. In a wide skillet add the cream, lemon juice, lemon zest, and goat cheese. Heat over medium high heat until the cream begins to bubble then turn down to medium low. Cook and stir until the goat cheese has melted into the sauce. Season with kosher salt and pepper. Keep the sauce on low heat until the pasta is cooked.
Once the water has boiled add the linguine and cook according to package ingredients. If you are planing to drain the pasta then remove about a cup of the cooking water before you drain it. Otherwise use tongs to lift the cooked linguine and add it directly to the sauce.
Toss the pasta in the sauce to coat, adding about ½ a cup of cooking water to thin the sauce. Add the chopped fresh basil and toss to mix in. If the sauce still feels too thick then add a bit more of the cooking water.
Serve the pasta topped with the balsamic roasted tomatoes and enjoy!