Position a rack in the lower third of the oven and preheat the oven to 350°F. Line the pan with paper liners.
To make the cupcakes, grate the zest of the lemon in the bowl of an electric mixer fitted with the paddle attachment (or in a mixing bowl if using a handheld mixer). Add the sugar, eggs, and salt. Beat at medium-high speed until the mixture is thickened and lighter in color, about 2 minutes. Or beat with a handheld mixer on medium-high speed for 3 to 4 minutes.
Add the rice and oat flours, baking soda, baking powder, cinnamon, nutmeg, zucchini, and dill and beat on low speed just until blended. Beat in the olive oil. Divide the batter evenly among the cups.
Bake until a toothpick inserted in the center of cupcakes comes out clean and dry, 18 to 20 minutes. Set pan on a rack to cool for a few minutes before tipping cakes out onto the rack to cool completely before icing or storing.
To make the frosting, put the dill into the bowl of a food processor fitted with the steel blade. Add 5 or 6 tablespoons of the powdered sugar and process until the dill is pureed, scraping the sides of the bowl as necessary, and adding a little more sugar as necessary until the mixture is a thick syrupy puree. Grate the zest of the lemon directly into the processor bowl and add the remaining sugar and the butter in chunks. Process until smooth and spreadable. Process until completely smooth and spreadable, scraping down the sides of the bowl as necessary. Add the olive oil and pulse to blend.
Note: I always try to sneak in a little more extra-virgin olive oil—it adds a lovely dimension and complexity to the frosting that ties into the cupcakes—but at some point, too much oil will curdle the frosting. If that happens to you, smooth out the frosting by pulsing in a bit more powdered sugar.
My career was sparked by a single bite of a chocolate truffle, made by my Paris landlady in 1972. I returned home to open this country’s first chocolate bakery and dessert shop, Cocolat, and I am often “blamed” for introducing chocolate truffles to America. Today I am the James Beard Foundation and IACP award-winning author of ten cookbooks, teach a chocolate dessert class on Craftsy.com, and work with some of the world’s best chocolate companies. In 2018, I won the IACP Award for Best Food-Focused Column (this one!).