First, begin making the crust. Grease and lightly flour a 9-inch tart pan and set it aside. Mix together the flour, sugar, and salt in an electric mixer with the paddle attachment on low speed until blended. Turn the mixer off, remove the paddle attachment, and attach the dough hook attachement. Cut the butter into pea-sized pieces over the bowl. Once all the butter has been cut into the bowl, turn the mixer on medium speed and allow to run for 1 minute. Then add the egg and almond extract and mix until a smooth dough just forms, but do not continue beating past that point. Remove the dough from the bowl and place it on a well-floured plate. Cover it and place it in the freezer to relax for a half an hour.

Meanwhile, you can begin candying the kumquats. Heat the sugar, water, and vanilla extract over medium heat in a wide and shallow pan until the sugar dissolves and the mixture begins to boil, stirring every 3 minutes. Once it's boiling, reduce it to a simmer and gently place the kumquat slices in the pan in a single layer. Allow them to simmer for 30 minutes. Remove them with a mesh or slotted spoon and place them on a wire rack with a plate or paper towels underneath to catch the dripping syrup.

Roll the chilled dough out onto a greased and well-floured piece of parchment paper, rolling it into a 12-inch square or circle (depending on the shape of your tart pan), flouring and reflouring your rolling pin as needed. Once rolled out, flip the sheet of parchment paper over onto the tart pan and peel it off. Press the dough into the pan and smooth it out with your fingertips as best you can (careful though, it's a bit sticky.) Trim off any excess dough hanging off the edges. Cover the pan and place it in the freezer for 30 minutes to relax.

Preheat the oven to 375 degrees Fahrenheit. To make the cream cheese filling, beat the sugar and cream cheese in an electric mixer fitted with the paddle attachment at low speed until smooth. Add the remaining ingredients and beat until just blended, taking careful not to over-beat them. Set aside.

Remove the plastic wrap from the tart crust and puncture the shell in several places with a fork. Place the shell in the oven and bake for 20 minutes. Remove it, pop any air bubbles that may have risen with a fork and allow them to air out until flat. Carefully spread the cream cheese mixture into the tart shell. Place the tart back in the oven and bake for another 15-20 minutes, or until the crust turns golden brown around the top edges. Remove and allow to cool completely before decorating with the candied kumquats. Serve at room temperature or chilled