Preheat oven to 400º. Halve the pumpkin, scoop out seeds and discard. Cut into 8 to 10 thick wedges. Place on a parchment-lined baking sheet, drizzle with 3 tablespoons of oil and season with salt. Roast until almost completely tender (you should be able to stick a fork in with just a bit of resistance), 20 to 25 minutes. Let cool.
When cool enough to handle, use a paring knife to carefully remove the skin from the pumpkin. Roughly chop the pumpkin into 2 inch pieces. Find some more tender pieces and mash enough to fill a ¼ cup measure and set aside.
In a large Dutch oven or other heavy-bottomed pot heat 2 tablespoons of the oil over medium-high. Once the oil is shimmering, add red curry paste and cook, stirring often, until fragrant and has darkened in color, 2 to 3 minutes. Reduce heat to medium-low, stir in coconut milk and simmer about 3 minutes more. Remove from heat and let cool slightly.
Add mashed pumpkin and ¼ cup water to coconut mixture and, using an immersion blender, puree until smooth. (Alternately, transfer mixture to a regular blender, and puree until smooth; return sauce to pot.).
Add green bell pepper, red bell pepper, shallot, chili, and bamboo shoots to the pot. Bring mixture to a boil, reduce heat to medium-low and simmer, covered, until the veggies have begun to soften, 5 to 7 minutes. Uncover and add reserved pumpkin and simmer until tender, about 5 minutes.
Just before serving, stir in lime juice, fish sauce and Thai basil leaves. Ladle curry over white rice and top with sliced basil. Serve with lime wedges.