Heat 2 tablespoons of extra-virgin olive oil in a large skillet over medium heat. Once the oil shimmers, add finely chopped shallots and cook for about 3 minutes, stirring frequently, until they soften and become translucent.

Next, stir in a small diced pear, maple syrup, and 1/4 teaspoon of kosher salt into the shallots. Cook the mixture for an additional 3 minutes.

Pour in the white balsamic vinegar and let the chutney simmer for 8-10 minutes, stirring occasionally, until the pears become tender.

Once the chutney has simmered, stir in finely chopped fresh rosemary and mix well.

In the same skillet, add the remaining olive oil and arrange the trimmed and halved Brussels sprouts cut-side down. Cook them undisturbed for about 4 minutes.

Toss the Brussels sprouts gently and continue cooking for another 5-7 minutes, until they are crisp-tender and cooked through.

Return the pear chutney to the skillet with the Brussels sprouts, folding them together gently to incorporate the flavors. Cook for an additional minute to warm everything through.