How to draw a border / outline around a QPixmap

Question

I am trying to add a black border around a QPixmap. I dumbly thought scaling it down would do it, but this wasn't the case, as you can see here:

I've tried a bunch of things, QGraphicsPixmapItem(), QGraphicsDropShadowEffect(), but I think I'm missing something. I need to create a drop shadow effect, or something, and then paint that back under the QPixmap, somehow. Or fill outward for only a few pixels?

Here is some code that I've been working with:

icon = "iconpath/icon.png"
base_pixmap = QtGui.QPixmap(icon)
color = QtGui.QColor("green")

# set black outline
mask = base_pixmap.createMaskFromColor(QtCore.Qt.transparent, QtCore.Qt.MaskInColor)
base_pixmap.fill(QtGui.QColor("black"))

# set mask
base_pixmap.setMask(mask)

# Take icon, edit size, add to pixmap
pixmap_image = QtGui.QPixmap(icon)

mask = pixmap_image.createMaskFromColor(QtCore.Qt.transparent, QtCore.Qt.MaskInColor)
pixmap_image.fill(color)

# set mask
pixmap_image.setMask(mask)

painter = QtGui.QPainter(self)
margin = 10  # shrink image to fit inside border
height_percent = (float(base_pixmap.height()) / 100) * float(margin)
width_percent = (float(base_pixmap.width()) / 100) * float(margin)

painter.drawPixmap(QtCore.QRect(width_percent / 2, height_percent / 2,
                                self.width() - width_percent,
                                self.height() - height_percent),
                   pixmap_image)

painter.end()