Toast chiles in a dry skillet over medium-high heat, turning occasionally and pressing down to help them make contact with the pan, until darkened in color and beginning to soften, about 3 minutes. Transfer to a bowl with 2 cups boiling water. Let sit for 30 minutes to soften. Drain, remove seeds and stems. Place in blender with the chicken broth and puree until smooth. Set aside.
Heat 1 tablespoon oil in a heavy pot over medium high. Season beef with salt and pepper and cook, stirring occasionally, until browned all over, about 5 minutes. Continue to cook until liquid has evaporated, about 3 more minutes. Transfer to a plate.
In the same skillet, add 1 tablespoon oil and cook onions and garlic, season with salt and pepper and cook until softened, stirring often. Add cumin and oregano and cook for another minute.
Add beef and beer to the pot with the onions. Bring to a boil, reduce heat and simmer, stirring occasionally, until almost completely reduced. Add chili puree, season with salt and pepper and bring to a boil again. Reduce heat and simmer until liquid is slightly thickened and the meat is tender, 20-25 minutes. Add squash and cover. Cook until the squash is tender, 20-30 minutes.
While the chili is cooking, toast pumpkin seeds sprinkled with olive oil and salt. Serve chili with pumpkin seeds and avocado.