Preheat the oven to 325F
Lightly butter 2 8" round cake pans and line the bottom of the pans with parchment rounds if you have them.
In a small saucepan, bring the milk to a simmer (barely bubbling around the edges).
Add the lavender, butter, and oil and remove from the heat. Set aside to steep.
Combine the flour, salt, baking powder, baking soda, and set aside.
Beat the eggs and sugar in a mixer until thick and creamy and light gold in color. The mixture should fall in ribbons from the whisk or beaters.
Add the dry ingredients to the mixture in the bowl and mix — by hand or on low speed of a mixer — just enough to combine. Scrape the bottom and sides of the bowl, then mix again briefly, to fully incorporate any residual flour or sticky bits.
Strain the lavender out of the milk mixtures and then slowly mix the lavender milk/butter/oil into the batter, stirring on low speed of a mixer until everything is just smooth.
Divide the batter evenly between the two pans.
Bake about 35 to 40 mins or until a toothpick inserted into the middle comes out clean. If you're using an instant-read thermometer (highly recommend this) the internal temperature of the cake should be 210F.
Let the cakes cool in the pan for 15 mins and then turn out onto a rack and let them cool to room temp.
Once the cakes are completely cool, brush them with the lavender syrup. Be generous. The syrup is doing double duty: adding more lavender flavor and also adding moisture to the cakes. Gluten free cakes can be dry and sandy in texture and this really helps.
Wrap the cakes tightly in plastic and refrigerate them overnight or at least for a couple of hours. This helps set the crumb and let the flavor develop. A chilled cake is also easier to frost.