Bring broth to a simmer in a saucepan over medium heat.
Heat 2 tablespoons butter in a Dutch oven or pot over medium. Add onion, season with salt, and cook until softened and translucent, 5–7 minutes. Add garlic and cook 30 seconds. Add rice, and cook, stirring constantly, until edges become translucent, 3 minutes.
Add wine to rice, and cook, stirring constantly, until fully absorbed. Stir in 4 cups warm broth, reduce heat to medium-low, cover, and simmer risotto until most of liquid has been absorbed, about 16 minutes, stirring twice.
Add remaining 1 cup broth to risotto and stir until creamy, 3–4 minutes.
Off heat, stir in peas, sugar snap peas, Parmesan, and remaining tablespoon butter, cover, and let stand 5 minutes. Stir parsley and tarragon into risotto; season with salt and pepper.
Top servings with pea shoots and poached eggs; serve with lemon wedges.