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Prepare the mapo tofu sauce: If the tofu came as a block in water, discard the water. Cut the tofu into large chunks, then use a stand blender or immersion blender to whirl the tofu into an ivory smoothie.
In a medium (3- or 4-quart) pot over medium heat, toast the Sichuan peppercorns for 2 to 3 minutes, until super fragrant and slightly darkened. (A wisp of smoke is OK.) Let cool briefly, then pound with a mortar and pestle or pulse in a spice grinder.
Prepare the remaining sauce ingredients and set them near the stove.
Warm the oil in the pot over high heat. When shimmering, add the meat. Stir and mash into cooked and crumbly pieces, 1 to 2 minutes. Add 2 1/2 tablespoons doubanjiang, the douchi (if using), ginger and red-pepper flakes (if using). Fry about 2 minutes longer, stirring constantly, until the mixture is a rich reddish brown.
Reduce the heat to medium-low, then stir in the soy sauce and sugar. Scrape in the blended tofu. (If there’s much left in the blender jar, add 1 tablespoon water and whirl to loosen it.) Stir to combine well, partly cover and bring to simmer. Cook for about 3 minutes, stirring occasionally, to develop flavor throughout. Expect orange oil to appear on top.
Taste the sauce and if needed, add the remaining 1/2 tablespoon doubanjiang (for heat), or a pinch of salt (for savoriness) or sugar (to tame heat).
Stir in the scallions, then add the cornstarch slurry and stir until thickened. Turn off the heat. Stir in half the crushed Sichuan peppercorns to seed a bit of zing. Let sit for 5 to 10 minutes to deepen flavor and color before using; a little lingering orange oiliness is normal. Makes about 2 1/2 cups. (You can also cool completely then refrigerate in an airtight container for up to 3 days.)
Prepare the spaghetti: Fill a large pot about halfway with water and add no more than 1 tablespoon of salt to lightly season. Bring to a boil over high heat, then add the spaghetti and boil until al dente according to package instructions. Ladle out about 3/4 cup of the pasta cooking water, then drain the spaghetti. Briefly rinse to remove some of the starch and shake to expel excess water.
In the same pot (or a clean large skillet, if you wish), warm the tofu sauce and 1/3 cup of the reserved pasta cooking water over medium heat. When hot and bubbling, add the spaghetti to the sauce. Use tongs to stir and coat the strands. Stir in extra pasta water by the tablespoon for a creamier, silkier finish, if desired.
When satisfied, stir in the scallion and cook very briefly until just softened. Divide the pasta among plates or shallow bowls and serve topped with the cheese and the remaining ground peppercorns.