Cook broccoli in a pot of boiling water until just tender, 3 to 4 minutes. Drain.
Heat 2 tablespoons oil in a large skillet over medium-high heat. Add shiitakes and baby bellas, sprinkle with salt and cook, stirring often, until deeply brown in spots, 5 to 8 minutes.
Reduce heat to medium; add garlic and the remaining 1 tablespoon oil and cook, stirring, for 30 seconds. Add vinegar and tamari and cook for 30 seconds more.
Remove from heat; stir in butter, then add the broccoli and crushed red pepper and gently toss to combine.