My daughter was born with a port-wine stain on the cheek. She is otherwise healthy. Facial port-wine stains are treated with laser therapy. Several sessions usually are needed. This treatment is more effective when initiated in the early years of life.
Laser treatment can be painful, so a topical anesthetic is used.
If this is inadequate, general anesthetic is necessary. My teenaged son has a pyogenic granuloma on his finger. It was burned out but recurred rather rapidly. Pyogenic granulomas are notorious for recurring after treatment, because the conelike blood vessel formations extend into the skin. If a portion of the PG remains in the skin after treatment, it returns.