Place the beetroot into a saucepan with enough water to cover by 3cm; bring to a boil. Reduce heat to medium-low, cover and simmer until the beetroot are easily pierced with a fork, about 30 minutes.
Meanwhile cook the bacon in a large, deep frypan over medium-high heat until evenly browned, about 10 minutes; transfer the bacon to a paper towel-lined plate to drain, reserving the bacon drippings in the frypan. Roughly chop the bacon and set aside.
Add the drained beetroot and silverbeet to the reserved bacon drippings; cover the frypan, place over medium heat and cook until the silverbeet is tender, 3 to 5 minutes. Stir the chopped bacon and frozen peas into the beet mixture; continue cooking until the peas are cooked through, about 5 minutes. Sprinkle the feta cheese over the mixture; stir. Serve hot.