Spring Vegetable Pot au Feu for French Fridays with Dorie

I haven't been very regular with my French Fridays with Dorie posts lately. To be honest, I just haven't been all that inspired by the dishes (with the notable exception of the bacon, asparagus, and egg salad, which I wish I'd made, and the quiche, which I completely futzed with).

But her warm weather vegetable pot au feu really appealed to me, partly because it's more of a method than a recipe, and partly because of that lovely, squishy poached egg, which I'll get to in a moment.  The basic idea here is that you successively saute and simmer some spring veggies in chicken or vegetable broth to create layers of flavor, and finish the whole lot with chopped herbs or an herb coulis of your choice.