I've made this recipe at least a dozen times since I first found it, but I've made a number of modifications to suit my personal tastes. The most critical change relates to the amount of butter called for, and this relates to the moistness issue I've complained of. The recipe calls for 2 1/4 cups of butter (9 oz.). I've found that cutting the butter down to 1 3/4 sticks (7 oz.) produces a cake that's plenty moist, but not too moist and not too greasy. I always recalled Natalie's cake being slightly dryer, which I personally love, although I've found my friends prefer a moister cake. So while I haven't gone down to 6 ounces, I probably would if I thought I'd be the only one eating it (and I might anyway just to see what happens - I suspect it would still be plenty moist). I tried olive oil once, and enjoyed it, but it was too moist and I haven't worked on adjustments with respect to an olive oil version . . . another time.
Also, I have typically used vanilla bean, as called for by the recipe, but I have not detected any measurable difference when using vanilla extract. Now I always love seeing those specks of vanilla in a cake, but if you want to save a few $$$, then use 2 teaspoons of vanilla extract in place of the 2 vanilla beans.
The recipe also calls for superfine sugar . . . you can achieve this by running regular sugar in your Cuisinart and pulsing several times. I also don't pulse quite so many times and this slightly cuts down on the sweetness of the cake (because superfine is more densely packed when measured).
For the ground almonds, I use the Bob's Red Mill ground almonds - it's just too easy, and I don't think the almonds affect the moistness to any significant degree . . . pretty sure butter is the main culprit.
I also think the zest of two lemons and juice of one of the lemons results in a cake that's very lemon dominant. I love lemon, but in this cake I want to taste pine nuts, almond and lemon. In that respect, I have found that the zest of 1-1.5 lemons, and the juice of at most 1/2 of a lemon, is sufficient. Of course, this depends upon the size of the lemon. But hey, go ahead and taste the batter and see what you think.
I have also upped the amount of pine nuts (a must in my opinion) and I've also added some salt to the cake batter itself (a generous 1/8 teaspoon).
Finally, I also add some almond extract - no more than 1/8 to 1/4 teaspoon (again, taste to judge for yourself), and I think this gives me the perfect almond-pine nut-lemon-vanilla marriage that I seek.
So, in summary, my revised recipe looks like this:
1 3/4 sticks unsalted butter (7 oz., or even slightly less)
2 vanilla beans (or 2 teaspoons vanilla extract)
zest of 1-1.5 lemons, and juice from about 1/2 lemon
8 tablespoons pine nuts
1 1/4 cups (not quite so) superfine sugar
4 eggs
3/4 cups all purpose flour
1 cup ground almonds
1/4 teaspoon salt (plus 1/8 teaspoon in batter)
I think it comes pretty damn close to that amazing pine nut-almond cake from Pasticceria Natalina. If she ever publishes her version, I'll be curious to see how they compare.