How to Make It
Preheat a convection oven to 350°F (or a regular oven to 375°F).
Halve the pumpkin vertically. Scrape out the seeds and set aside; rub the interior of the pumpkin with olive oil and dust generously with salt.
Place cut side up on a baking sheet and bake for 30 minutes.
Flip the halves and bake for 20 minutes more. Let the pumpkin cool slightly.
When cool enough to handle, scoop out the flesh, transfer to a food processor, and puree until smooth. Set aside.
Meanwhile, wash the reserved pumpkin seeds well and measure out ½ cup (discard the rest or save for another use). Place the seeds in a bowl and drizzle with 1 teaspoon olive oil and ¼ teaspoon salt. Toss to coat.
Place a baking sheet in the oven for 5 minutes to preheat. Add the seeds to the hot pan and bake for 18 to 20 minutes, until crispy and lightly golden.
In a large saucepan, bring 4 cups water, the cream, and 1 teaspoon salt to a boil. Stir in the grits and reduce to a simmer. Cook, stirring occasionally, until the grits are tender and thick, about 50 minutes.
Remove from the heat and stir in the pumpkin puree, Parmigiano-Reggiano, and lemon juice.
Divide the grits among bowls, sprinkle the pumpkin seeds over each bowl, and drizzle with the maple syrup.