Bring a large pot of water to a boil and cook the penne according to the directions. In the last 3 minutes of cooking, add the broccoli so it will cook along with the pasta. Drain the pasta and broccoli.
Return the pot to medium-high heat and melt the vegan butter. Add in the garlic and cook for a minute just until garlic begins to brown. Remove from heat and stir in the lemon zest, lemon juice, salt, and crushed red pepper flakes. Add the pasta and broccoli back into the pot and toss well to combine. Garnish with slivered almonds and parmegan to serve.