Bring the broth to a low simmer in a saucepan.
Heat the olive oil in a large saucepan over medium-high heat until hot. Add the garlic and cook briefly until light brown. Add the onion and a pinch of salt, lower the heat to medium, and cook until the onion is soft but not brown, about 2 to 3 minutes. Add 2 cups of the simmering broth and bring to a boil. Add the pastina; stir well, and reduce the heat to maintain a slow simmer. Season with salt and pepper.
Simmer, ladling in the broth 1/2 cup at a time as the previous addition is absorbed, and stirring occasionally to prevent the pastina from sticking to the bottom of the pan, until the pasta is about three-fourths done, about 10 minutes. Add the peas and the remaining simmering broth and cook until the peas are tender and the pasta is al dente, about 3 minutes. Remove from the heat and add 1 tablespoon of the butter, the oregano, thyme, Parmesan, and 3 tablespoons of the bacon. Stir well. The consistency should be quite loose, like a thick soup.
During the last few minutes of cooking, stir in the carrot juice. Whisk in the remaining 1 tablespoon butter until just melted. Top with remaining bacon.