Take the asparagus spears, trim the ends, then cut them in half. Blanch or steam for five minutes. Rinse with cold water when done and lay out on paper towel to dry a bit.
Open and drain the hearts of palm and cut each piece into four quarters. Set aside.
Slice the prosciutto in half lengthwise.
Take a piece of the prosciutto and lay it out on the work surface. Place a piece of asparagus along with a piece of the hearts of palm and lay them together at one end of the prosciutto. Roll them up at an angle so the prosciutto wraps from the top to the bottom.