In a small saucepan, whisk together the water and 2 tablespoons of flour over medium heat. Whisk constantly until the mixture thickens into a paste. Remove from the heat and set aside.
Meanwhile, in a measuring cup, heat the milk in the microwave for 30 seconds or until warm but not hot. Whisk in the sugar and yeast and set aside until the mixture is foamy on top, about 5 minutes.
Whisk the eggs and melted butter into the yeast mixture.
In the bowl of a stand mixer, whisk together the flour, salt, lemon zest, and thyme.
With the machine running (use your dough hook attachment), slowly pour in the yeast mixture and then the flour paste from the saucepan.
The dough should come together quickly and will be quite sticky. Resist the urge to add more flour at this point – it can yield a denser dough. Run the machine for about 5 minutes.
Gently transfer the dough to a lightly floured surface and knead by hand for another 5 minutes. You want the dough to be soft and smooth and no longer sticky at this point. Form the dough into a ball and place in an oiled bowl.
Cover and allow the dough to rest until it has doubled in size, about 1 hour.
Once the dough has doubled in size, gently pat it out with your hands on a lightly floured surface until it is about ½ inch thick. Using a 3-inch round biscuit cutter, cut out the donut rounds and place them on a parchment lined baking sheet.
Continue until all the dough has been formed, re-using and re-working any dough scraps. Once all the donuts have been cut out, cover the baking tray with a kitchen towel and set aside for 30 minutes to an hour, or until the donuts have doubled in size.
For the Filling:
While the donuts are rising, make the filling by combining the lemon curd, butter, and cream cheese in the bowl of your stand mixer (you can also use a hand mixer). Cream them together until smooth and fluffy, about 2 minutes.
Add in the zest and juice of the lemon and mix again.
Slowly add in the powdered sugar, 1 cup at a time, and beat until the mixture is thickened and fluffy. You want it to reach a “stiff peak” stage, which just means that it can hold it shape when the beater is raised up.
Fit a piping bag with a star tip and fill the bag with the filling. Set aside until the donuts are fried.
To Fry and Fill the Donuts:
Heat 2 inches of canola oil in a heavy-bottomed pot or Dutch oven over medium-high heat. Heat the oil to 350°F.
Gently and carefully add the donuts, 2-3 at a time (depending on the size of your pot), to the hot oil. Cook for 1 minute per side, or until they are deeply golden brown and crisp on the outside.
Place the fried donuts on a cooling rack set over a baking sheet lined with paper towels. Allow them to mostly cool before filling them.
To fill the donuts, cut a small slit in the side of each donut with a small paring knife. Insert the piping bag tip into the hole and gently squeeze the bag to fill the donuts.
Dust the filled donuts with powdered sugar once they have all been filled.
These are best if served immediately, but I found that they held up well if cooled completely to room temperature and then stored in an airtight container on the counter for a day or two.
Before serving, I reheated them in a 200F oven for about 10 minutes. Some of the filling might ooze out when you do this, but warming them up a bit really helps revive them to their original fried state.