Rub corn and zucchini lightly all over with oil. Grill over medium-high heat (or pan sear in cast iron pan) turning occasionally until zucchini and corn is lightly charred all over.
Transfer zucchini and corn to a cutting board and when cool enough to handle, cut kernels off of cobs and cut zucchini into 1/2-in cubes.
Heat a large skillet over medium heat. Add butter and swirl to coat pan. Add shallot and saute several minutes until softened. Add garlic and orzo and cook 1-2 minutes until orzo is lightly toasted.
Add broth to skillet and stir until evenly combined. Bring to a simmer over medium heat, then reduce heat to medium-low and allow to simmer 10-15 minutes until most of the liquid is reduced and orzo is tender, stirring occasionally.
Remove orzo from heat and stir in charred corn, zucchini, heavy cream, pesto, Parmesan, and basil until evenly combined.
Season orzo with salt and pepper to taste and serve warm with additional Parmesan and basil sprinkled on top. Enjoy!