Preheat oven to 350ºF. Put pecans on a baking sheet and toast in oven, shaking pan once or twice, until nuts smell fragrant, about 5 minutes. Cool and finely chop.
Reduce oven temperature to 200ºF. Line 2 baking sheets with parchment paper or foil.
Put egg whites and cream of tartar in the clean bowl of an electric mixer. Beat on medium speed until whites form soft peaks when beaters are lifted, 3 to 4 minutes. Gradually add sugar, beating until whites hold stiff peaks when beaters are lifted, 3 to 4 minutes more. Fold in toasted nuts, lemon zest, and vanilla.
Spoon meringue into a large ziplock bag, cut off a small piece of a corner, and squeeze meringue into 1 1/2-inch rounds on baking sheets.
Bake without opening the oven door for 1 hour and 15 minutes. Turn off oven and let meringues sit in the oven until cool, at least 1 hour or as long as overnight (you can turn off the oven just before going to bed and let the cookies cool in there until morning).
Serve immediately or store in an airtight container for about a day. The cookies will keep longest if the humidity is low.
Tip: Avoid making meringue cookies on a humid or wet day because the moisture in the air will be absorbed by the meringue and make the cookies sticky.