Ok, I hadn’t thought of that.
L1 is roughly 1 million miles away from the Earth in the direction of the Sun, roughly 1/100 of the distance (0.01AU). The Sun's diameter is roughly 100 times the diameter of Earth. This means that at L1, a parasol that is big enough to cast shade on Earth has to be TWICE the size of Earth, roughly 16,000 miles in diameter.
So you're not only talking about one HUGE FREAKIN' parasol, you're talking about one that is TWICE the size of Earth.
Ain't happenin'.