3 teaspoons extra-virgin olive oil, divided
2 large shallots, chopped (about ½ cup)
8 ounces Brussels sprouts, trimmed and halved (about 2 cups)
2 tablespoons water plus 1½ cups, divided, plus more as needed
3 medium cloves garlic, finely chopped (1 tablespoon)
8 ounces whole-wheat spaghetti
2½ cups unsalted vegetable broth
1⅔ cups finely grated Asiago cheese (about 2½ ounces), plus more for garnish
¾ cup heavy cream
⅛ teaspoon crushed red pepper, plus more for garnish
⅛ teaspoon salt
2 tablespoons thinly sliced fresh basil
Heat 2 teaspoons oil in a large skillet over medium heat. Add chopped shallots; cook, stirring often, until fragrant, about 1 minute. Add halved Brussels sprouts and 2 tablespoons water. Cover and cook, stirring occasionally and adding 1 tablespoon water at a time as needed to prevent burning, until bright green and tender, 5 to 8 minutes. Stir in chopped garlic and the remaining 1 teaspoon oil. Cook, uncovered and stirring constantly, until fragrant, about 30 seconds. Transfer the mixture to a medium heatproof bowl. Wipe the skillet clean.
Combine 8 ounces pasta, 2½ cups broth and the remaining 1½ cups water in the skillet. Cover and bring to a boil over high heat. Boil, covered, stirring occasionally, until the pasta is al dente and the liquid is nearly absorbed, about 12 minutes.
Stir in 1⅔ cups Asiago, ¾ cup cream, ⅛ teaspoon crushed red pepper and ⅛ teaspoon salt. Cook, stirring constantly, until the sauce thickens, 2 to 4 minutes. Remove from heat and return the Brussels sprouts mixture to the skillet. Using tongs, toss to coat evenly. Sprinkle with 2 tablespoons basil. Garnish with additional crushed red pepper and/or Asiago, if desired.