Field Garlic (Allium vineale): At this time of year, the most delectable field garlic parts are the scape and bulb (the middle 'chive' section is too tough). Use in place of green garlic. Scapes are especially great grilled, pickled, or pestoed. 

American Groundnut (Apios americana): Starchy tuber that must be cooked. Best peeled, but not a necessary step, especially with the tiny tubers. They also tend to burst open once boiled, making it easy to discard the skin.

Japanese Knotweed - see below

OR Milkweed Shoots (Asciepisa syriaca):

All about Milkweed

Lamb's Quarters (Chenopodium berlandieri): A delicious, prolific, and nutritious spinach substitute.

Garlic Mustard leaves (Alliaria petiolata): The leaves included in this share are extra large and especially great for stuffing like grape leaves. 

Spruce tips - see below

Dame's Rocket flowers (Hesperis matronalis): This pretty, invasive, spicy flower makes a great salad addition

Black Locust flowers (Robinia pseudoacacia): This super ephemeral jasmine-like flower makes amazing ice cream, mead, and so much more.

Stinging Nettles - see below

Monarda leaves - see below

Spicebush twigs and leaves (Lindera) : the twigs and leaves of this fragrant bush make excellent tea. Just don't dry them out  - they'll lose their flavor.

Wood Sorrel (Oxalis acetosella): This tender, sour green is a favorite among the youngest foragers. Best eaten raw in a salad, but also makes fantastic pesto or lemonade.

Chickweed - see below