Fill a large saucepan with a few inches of water and bring to a simmer over medium heat.
In a large heat-proof bowl, whisk together the 3 whole eggs, 3 egg yolks, 1 cup sugar, the lemon zest, lemon juice, and a pinch of salt.
Place the bowl over the pan of simmering water and cook, stirring constantly with a wooden spoon, for about 10-15 minutes. (Once the mixture starts to thicken a tiny bit you may want to switch to a whisk to stir it).
Remove from heat and set aside for 15 minutes.
Place a piece of plastic wrap directly on the surface of the mixture and refrigerate for at least 1 hour or until completely chilled.
Place the 3 remaining egg whites in a mixing bowl and beat on high speed for 1 minute.
Add remaining 2 tablespoons of sugar and continue to beat until the whites are stiff. Carefully fold the beaten whites into the cold lemon mixture.
Place the cream in the same bowl the whites were in and beat on high speed until stiff peaks.
Carefully fold the whipped cream into the lemon mixture. Chill and serve cold with sweetened whipped cream.