In a pan over high heat, bring the stock to a boil, then lower the heat to low.
In a medium-size paella pan or large skillet over medium heat, heat the oil and add the onion, garlic, carrot, saffron, and paprika. Sauté the mixture, stirring occasionally, for 7 minutes. Add the bell peppers, sliced mushroom tops, wine, salt, and rice. Stir to combine, then sauté, stirring occasionally, for another 5 minutes.
Pour the stock over the rice and increase the heat to high. Bring the rice to a boil, then lower the heat to low, while stirring. Cover the pan with foil and allow the rice to cook over low heat for 18 minutes, then turn off the heat. Leaving the foil on the pan, allow the rice to steam with no heat for another 15 minutes.
While the rice is cooking, brush the sausage, mushroom stem rounds, and tomatoes with oil, and top with additional salt and black pepper. Grill over high heat. The tomatoes will take about 5 minutes, and should only be grilled on the flat side. The sausage and mushrooms will take about 8 minutes, and should be turned halfway through. Remove the items from the grill, slice the sausage, and cut the tomatoes into quarters.
Remove the cover from the paella and arrange the sausage, mushrooms, and tomatoes on top. Garnish with the parsley, peas, and lemon wedges.