Preheat oven to 375°F (190°C). Line a 12-cup muffin tin with paper liners or grease and flour it.
In a large bowl, whisk together the flour, sugar, baking powder, and salt.
In a separate medium bowl, whisk together the eggs, milk, vegetable oil, lemon juice, and lemon zest.
Pour the wet ingredients into the dry ingredients and mix until just combined. Do not overmix.
In a small bowl, beat the softened cream cheese and sugar until smooth. Beat in the egg and vanilla extract until combined.
Fill each muffin cup about two-thirds full with the muffin batter.
Dollop about 1 tablespoon of the cream cheese mixture onto the center of each muffin. Use a toothpick or knife to gently swirl the cream cheese into the batter.
Bake for 20-25 minutes, or until a toothpick inserted into the center of a muffin comes out clean.
Let the muffins cool in the tin for a few minutes before transferring them to a wire rack to cool completely.
Notes
These muffins are best served fresh, but can be stored in an airtight container at room temperature for up to 2 days.