Bring pot of water to boil on stove.
Add corn to boiling water and boil for about 10 minutes.
Meanwhile preheat grill or grill pan by heating to high heat.
Prepare zucchini by tossing in a bowl with a glug of olive oil and salt and pepper, to taste. Set aside.
To grill: Place lemon and zucchini on the grill. Grill for about 2 minutes per side, or until tender and lightly charred. Transfer to plate and tent with foil to keep warm.
Once corn is cooked, drain and immediately transfer to hot grill, periodically turning, until lightly charred all over - about 5 minutes total. (Note - grilling the corn is optional, it will be cooked fully after boiling).
Remove lemons and corn and let cool briefly. When cool enough to handle, slice the corn from the cob and add corn to the plate with zucchini. When lemons are cool enough to handle, juice the lemons and reserve the juice for later.
Refill the pot of water, add salt, and bring to boil. Add linguine and boil for 10 minutes (or per package instructions).
While boiling linguine, prepare your alfredo sauce. In a skillet, bring heavy cream to simmer over medium heat. Add half of the parmesan and melt into the cream. Reduce heat to low, and simmer until mixture is thickened and coats the back of the spoon. Turn off heat and add about 1 tablespoon of lemon zest, juice from the caramelized lemons, remaining parmesan, nutmeg, and salt and pepper, to taste. Mix in about 1/4 cup of additional hot pasta water and stir to combine.
Add pasta to skillet with sauce. Add vegetables and toss to combine. Top with pine nuts and parsley, and additional black pepper, as desired.