Preheat the oven to 425°F.
Toss the mushrooms with 2 tablespoons of the olive oil, half the garlic, rosemary, thyme, red pepper flakes, and a pinch of salt. Spread on a sheet pan in a single layer.
Roast the mushrooms for 15 minutes, until softened and lightly browned at the edges.
While the mushrooms roast, pat the tuna steaks completely dry and rub with the remaining olive oil, remaining garlic, salt, and pepper.
Remove the sheet pan from the oven and push the mushrooms to one side.
Switch the oven to broil, or raise the temperature to 500°F if your oven has no broiler setting.
Arrange the tuna steaks on the open side of the pan and return to the oven.
Broil for 2 to 3 minutes per side, until the outside is browned and the center is still pink through a cut.
Remove from the oven and drizzle the tuna and mushrooms with lemon juice.
Garnish with fresh basil and serve immediately.