Preheat the oven to 350°F (175°C). Roll out the pie crust, fit it into a 9-inch pie pan, crimp the edges, and prick the bottom with a fork.
Blind bake the crust until lightly golden, then remove from the oven and set aside.
If using fresh broccoli, blanch briefly until bright green, then cool and dry completely. If using frozen broccoli, thaw fully and squeeze out all excess moisture.
In a large bowl, whisk together the eggs, heavy cream, Dijon mustard, dill, salt, and black pepper until smooth.
Spread the broccoli evenly over the baked crust, then sprinkle the shredded cheddar cheese on top.
Slowly pour the egg mixture over the filling, stopping if the crust becomes full.
Bake for 35–45 minutes, until the top is lightly golden and the center is just set with a slight jiggle.
Remove from the oven and let rest for 10–15 minutes before slicing and serving.
