Preheat your oven to 375 degrees Fahrenheit to ensure it reaches the right temperature for baking. Meanwhile, line your muffin pans with paper cups so they're ready for the batter.
In a large bowl, whisk together the canola or vegetable oil, white sugar, and pure vanilla extract until fully incorporated. Add the canned pumpkin puree, eggs, and milk. Whisk until the mixture is smooth and well combined.
In a separate bowl, mix the all-purpose flour, baking soda, baking powder, table salt, and ground pumpkin pie spice. Gradually add this dry mixture to the wet ingredients, whisking until just combined. Be careful not to overmix, which can make the muffins dense—I always stop mixing as soon as no dry spots remain.
In a separate large bowl, beat the cream cheese block and granulated sugar together using an electric mixer until smooth and creamy. Add in the egg and vanilla flavoring, and continue mixing—scraping down the sides of the bowl as needed—until the filling is uniform. Set aside until ready to use.
Using a #24 scoop or by filling muffin cups about 2/3 full, scoop the pumpkin muffin batter into the prepared muffin cups. Top each with a spoonful of the cream cheese filling (about a #50 scoop or a bit more than 1 tablespoon per muffin). Using a butter knife, gently fold (not swirl) the two batters together: insert the knife through the center of the muffin batter and scrape along the bottom, then draw the knife out at the edge and fold the batter back toward the center. Repeat 2 to 3 times to create a marbled effect; less mixing gives the best look.
Bake the assembled muffins in the preheated oven at 375˚F for 15-18 minutes, or until a toothpick inserted in the center comes out with a few moist crumbs. Avoid over-baking to keep the muffins moist. Once baked, let the muffins cool completely before serving. I like to let them cool in the pan for a few minutes, then transfer them to a wire rack for best texture.