1. Position racks in upper and lower thirds of oven; preheat to 425°F (220°C). 2. Trim and halve Brussels sprouts; toss with 1 tsp (5 mL) oil in a medium bowl. Spread in a single layer on half of a large rimmed baking sheet. Toss fennel in the bowl with another 1 tsp (5 mL) oil; spread on the other half of the pan. Toss carrots in the bowl with another 1 tsp (5 mL) oil and spread on half of a second rimmed baking sheet. Toss beet slices with another 1 tsp (5 mL) oil; spread on the other half of the pan. Sprinkle the vegetables with 1/2 tsp (2.5 mL) salt.
3. Roast the vegetables, stirring once halfway through and rotating the baking sheets top to bottom and front to back, until soft and beginning to caramelize, 25 to 30 minutes. Arrange on a serving platter.
4. Meanwhile, mash garlic and the remaining 1/2 tsp (2.5 mL) salt in a small bowl with the back of a spoon until a paste forms. Add lemon juice, capers and anchovy (if using). Whisk in the remaining 2 tbsp (30 mL) oil; drizzle over the vegetables.