Dice fennel into ¼-inch cubes (reserve fronds), roughly chop tomatoes, mince garlic, and finely dice onion. Pour vegetable stock into a medium saucepan and bring to a gentle simmer, then reduce heat to low to keep warm throughout cooking.
Heat 2 tablespoons olive oil in a large heavy-bottomed pot over medium heat. Cook fennel 5–6 minutes until softened, add onion and cook 3 more minutes, then stir in garlic for 30 seconds until fragrant. Season lightly with salt.
Add Arborio rice to the pot and stir constantly for 2–3 minutes until the grains are slightly translucent around the edges and look almost pearly. Don't skip this step — properly toasted rice absorbs liquid more evenly.
Pour in the white wine and stir constantly, scraping up any bits from the bottom, until the wine is almost completely absorbed, about 2–3 minutes.
Stir in the chopped tomatoes, their juices, and the remaining 1 tablespoon olive oil. Cook 3–4 minutes, stirring frequently, until the tomatoes begin to break down into a sauce. Season with salt and pepper.
Add one ladle (about ½ cup) of warm stock and stir continuously until nearly absorbed before adding the next; repeat this process, maintaining a gentle simmer and stirring constantly throughout.
Continue adding stock one ladle at a time and stirring for 18–20 minutes total, tasting after 18 minutes; the rice should be tender with a slight bite in the center and the consistency should be loose and flowing, not stiff.
Remove from heat and vigorously stir in the butter and freshly grated Parmesan (mantecatura) until fully emulsified and the risotto is glossy and velvety. Taste and adjust seasoning, then rest 1–2 minutes before serving.
Spoon into shallow bowls immediately and top with torn fresh basil, fennel fronds, a drizzle of olive oil, and extra Parmesan on the side. Risotto waits for no one — serve right away.