In a large pot, bring salted water to a rolling boil. Add trimmed tenderstem broccoli and asparagus; cook for 3 minutes until bright green and just tender. Use a slotted spoon to remove and set aside while keeping water boiling.

In the same boiling water, add linguine and cook according to package instructions (about 8-10 minutes) until al dente. Reserve a cup of pasta water, drain the rest, and return pot to heat.

In a large skillet, melt butter over low heat. Add a splash of olive oil and sliced garlic, sauté gently for 30 seconds until fragrant but not browned.

Squeeze juice of half a lemon into pan, add broccoli, asparagus, and capers, tossing carefully to combine. Remove from heat when well-coated.

Add drained pasta to skillet, sprinkle in Parmesan cheese and a splash of reserved pasta water. Toss until combined and season to taste with salt and pepper. Serve immediately.