Preheat oven to 350 F.
Line your desired cake pan with parchment paper.
In a medium mixing bowl, whisk together eggs, yogurt, olive oil, vanilla, lemon juice, zest, and thyme leaves. Once combined, add in sugar and whisk until dissolved.
Fold the flour mixture into the wet ingredients, stirring until just combined.
Transfer the batter to the lined baking dish.
Bake at 350 F for 25-35 minutes, until cooked through. The cake will press back like a sponge with a gentle touch and appear slightly golden on top.
While the cake bakes, prepare the glaze.
In a small mixing bowl, stir together the lemon juice and powdered sugar. Add 1 tablespoon of milk if needed, to reach your desired consistency. (that of liquid glue)
When the cake is finished, allow to cool completely. Transfer to a cake plate and drizzle the glaze over the top of the cake, garnish with additional thyme leaves.