Preheat your oven to 375 degrees F.
Line a 15x10 inch jelly roll pan with parchment paper. There should be extra paper hanging off the sides of the short end of the pan, and the paper should line up with the long edges of the pan. See photo. Spray the paper and sides of the pan well with nonstick spray.
In a large bowl or stand mixer, add 3 eggs. Beat for 3-4 minutes on medium speed until the eggs are pale and bubbly. Well-beaten eggs make for a light and fluffy cake!
Add 1 cup granulated sugar. Beat well. Add 2/3 cup pumpkin. Beat well.
Add lemon juice and vanilla. Beat until combined, scraping the sides and the bottom of the bowl.
In a small bowl, whisk together flour, baking powder, salt, cinnamon, ginger, cloves, nutmeg, and cardamom.*
Add the flour mixture and beat until very well combined, scraping the sides of the bowl.
Pour the batter into the prepared pan and smooth to the edges.
Bake at 375 for 13-15 minutes. Insert a toothpick in the center of the cake. If it comes out with no batter on it, the cake is done. It should spring back when you press on the center. The edges should look set but take it out before they look crispy! It's important for your cake to be baked all the way through, but over baking it will make it more difficult to roll, so keep a close eye on it.
Clear a work space on your counter. Have a bowl of powdered sugar ready to go.
Within one minute of taking the cake out of the oven, sprinkle the entire top of the cake with plenty of powdered sugar. Fold the edge of the parchment paper that is hanging out of the short end of the cake over the cake. Start rolling up the cake on the short end, rolling the parchment paper. You don't need to roll it super tight. Add more powdered sugar as necessary.
Once your cake is completely rolled up, wrap the whole thing in plastic wrap so that it doesn't dry out, then let it cool for 1-2 hours. You can put it in the fridge to speed it up if you want. Let the cake sit at room temperature for a few minutes before unrolling though.
While the cake is cooling, prepare the cream cheese frosting. In a large bowl or stand mixer, beat the softened cream cheese until smooth, about 1 minute. Scrape the sides and bottom of the bowl.
Add the softened butter and beat until smooth, scraping as you go.
Add 2 cups powdered sugar, 1 teaspoon vanilla, and 1/4 teaspoon salt. Beat until smooth, scraping the edges. Cover and store in the fridge until you are ready to frost the cake. (If your frosting is too warm when you roll up your cake, you risk it oozing out the sides.)
When your cake is cool, unroll completely and frosting the entire inside of the cake. Make sure to add plenty of frosting to the edge of the cake that is going to be rolled up in the center. Spread the frosting right to the edges of the cake.
Carefully roll up your cake again, without the parchment paper. Wrap it in plastic wrap again and chill for 1-3 hours until completely cool.
Use a sharp serrated knife to slice the cake into about twelve 1-inch slices. Wipe off the knife in between slices.
Store the cake covered in the fridge.
*You can use any spice blend you like! You can use about 1 and 1/2 tablespoons of pumpkin pie spice to replace the cinnamon, ginger, cloves, nutmeg, and cardamom if you prefer.