Preheat a grill or broiler. Grill or broil the corn until it is dark brown on all sides. Cut the kernels off the cob and reserve. Once the kernels have been removed from the cob, run your knife along the cob to get any residual pieces of the kernels. Reserve.
Coat a large wide pot, over medium-high heat, with olive oil. Toss in the garlic and crushed red pepper. When the garlic becomes golden and is very aromatic, remove it from the pan and discard. Toss in the cherry tomatoes and roll them around in the oil. Add 1 cup of stock and season with salt. Reduce the heat to medium and let the tomatoes cook until they start to burst and give off their juices. This will take about 8 to 10 minutes.
Bring a large pot of well-salted water to a boil over medium heat.
Add the corn kernels to the pot with the tomatoes. Stir to combine and add 1/2 cup of stock if the liquid level is very low.
Drop the pasta into the boiling water and cook for 2 to 3 minutes, or longer if using dried pasta. Toss the shrimp into the pot with the tomatoes and stir to combine.
Drain the pasta from the cooking water, reserving 1/2 cup water, and toss immediately into the pot with the tomato mixture. Add in 1/2 cup of the pasta cooking water, if needed. Toss vigorously to combine. Remove from the heat and give a drizzle of high quality finishing oil and a sprinkling of grated Parmesan. Transfer to a serving bowl or platter and serve immediately.