Heat the oven to 350°F. Line a standard muffin tin with paper liners, or lightly grease each muffin cup.
Measure the ingredients before beginning. If necessary, allow the eggs to reach room temperature so they blend evenly into the batter.
In a medium mixing bowl, whisk together 1/2 cup packed brown sugar, 2 teaspoons baking powder, 1/2 teaspoon salt, 1 teaspoon pumpkin pie spice, and 3/4 cup all-purpose flour.
Continue whisking until the baking powder and spices are evenly dispersed throughout the flour mixture. Set aside.
In a separate bowl, whisk together 1 can pumpkin purée, 2 room-temperature eggs, 2 tablespoons vegetable oil, and 1 teaspoon vanilla extract.
Mix only until the ingredients form a smooth, uniform mixture and no visible streaks of egg white remain.
Pour the pumpkin mixture into the bowl containing the dry ingredients.
Using a spatula, fold the mixtures together gently until they are just combined. The batter may retain a few small lumps; avoid excessive mixing, which can produce dense or firm muffins.
In a small bowl, combine 1/4 cup softened butter, 1/4 cup all-purpose flour, 1/4 cup granulated sugar, and 1 teaspoon ground cinnamon.
Work the ingredients together with a fork or fingertips until the mixture develops a coarse, crumbly consistency with several small, pea-sized pieces of butter remaining.
Divide the pumpkin batter among the prepared muffin cups, filling each approximately three-quarters full.
Distribute the cinnamon streusel evenly over the filled muffin cups.
Bake at 350°F for 18–20 minutes. The muffins are ready when the tops spring back lightly when touched and a toothpick inserted into the center emerges with a few moist crumbs. The streusel should also appear lightly golden and crisp.
Remove the muffin pan from the oven and allow the muffins to rest in the pan for 5 minutes.
Carefully transfer them to a wire cooling rack and allow them to finish cooling. Serve while slightly warm to retain the contrast between the tender pumpkin crumb and crisp buttery topping.