Bring broth to a rolling boil and add grits. Stir vigorously, then reduce heat to low and cover. Allow grits to simmer for 10 minutes, stirring occasionally.
Brown the butter in a small pot over medium heat. Let butter melt untouched, then whisk constantly once simmering. Simmer and brown, until butter is golden and fragrant. Remove from heat.
When grits have absorbed the broth, stir in milk, pumpkin puree, salt, pepper, sage and nutmeg. Continue to cook on the lowest setting for 5-10 minutes.
Stir in Parmesan cheese and browned butter.
Melt butter in a frying pan over medium heat. Crack eggs into the pan and turn heat to low until the yolk firms up and whites start to sizzle, browning slightly.
Portion pumpkin grits into bowls and top with crispy fried egg, Parmesan cheese, pepitas, and black pepper.