Resolving this too many forays into Google as I don't have the vocabulary to describe leaves, and my plant knowledge is truly quite pathetic.
I finally ran into an edible chrysanthemum, but that turned out to be a near miss. C. leaves are round while these leaves were spiky and two-tones. A little more research resolved the answer.
Mugwort. I've got Mugwort. The leaves of this plant are used in many Korean dishes, especially in the spring to early summer. So that means that we have yet more edible plants.
Meanwhile, the lawn is coming along. The previous owners had over-kept the lawn, and this year I'm finally seeing diversity return. The clover is encroaching, some of the tough patches have thinned out, and I'm seeing other weedy bits show up. Yay for diversity.
Since we just planted some apple trees, the dirt is all turned up around the trees, so I took the opportunity to plant some basil there as well. If we're going to get weeds, we're going to get the tastiest weeds that I can stack in my favor. I also tossed a little dill there for good measure. I'm rather a fan of fire and forget gardening, so they'll either grow or they won't.