Place sweet potatoes into a saucepan, cover with chicken broth, and bring to a boil. Reduce heat to low, cover, and simmer until sweet potatoes are tender enough to pierce easily with a fork, about 10 minutes.
Drain and return potatoes to pan; add butter and cover pan.
Cook and stir bacon in a large skillet over medium heat until browned and crisp, about 10 minutes.
Transfer bacon to paper towels to blot grease.
Process basil and almonds in a food processor until pulverized, about 30 seconds, and slowly drizzle olive oil into the running food processor until thick, 1 to 2 minutes.
Add lemon juice, salt, and black pepper to basil mixture and pulse several times to combine to make the pesto.
Beat sweet potatoes in a bowl with an electric mixer on medium speed, slowly adding milk, until potatoes are fluffy and smooth. Alternatively, mash sweet potatoes with a fork if you prefer a more chunky texture. Season to taste with more salt; stir in pesto and bacon.
