There are multiple farming mods and food mods in this pack that give a wide variety of options for filling your hunger bar. However, as well as monitoring your hunger bar, you must also watch your nutrition values (monitored with the N key by default). If any of your nutrition values fall too low, you will start to receive Debuffs, like Mining Fatigue. You can raise your nutrition values by eating certain foods. For example, milk can increase the Dairy value, and potatoes can increase your vegetable value.
Max Health Increase[]
As a result of the mod Spice of Life: Carrot Edition, the game keeps track of how many unique foods you have eaten. For every ten unique foods you eat, your max health will be increased by 1 heart, up to 60 additional hearts! Because of this, you'll want to eat one of each unique food that you come across (you can check how many unique foods you have eaten by using the command /foodlist size).
You can tell if you've eaten a food before; if you hover over a food item, in it's tooltip, there will be a message that says: "Not yet eaten. I wonder what it tastes like?" or "Eaten: assisted in adding hearts." The first one signifies that you have never eaten this food before and that you should probably eat it whenever you can; the second one signifies that you have eaten that food before, so eating it will not increase your max hearts further (though it will still fill your hunger and nutrition bars).
Early Foods[]
Early game, good food sources can be hard to come by. Thankfully, filling, nutritional foods from the Pam's Harvestcraft mod are common loot chest reward. As another early food method, you can find different "gardens" (plant-like blocks) throughout your world which when broken drop a few food vegetables from Pam's mod. You can also find trees with fruit on them and can then craft saplings using three of the same type of fruit with a vanilla sapling. Villages can also supply large amounts of food and seeds.
Protein[]
A good food source is rotten flesh dried on a drying rack (Crafted from 3 wooden slabs). This purifies them, allowing them to fill your hunger bar and Protein meter. Any animal meat is also useful for Protein.
Dairy[]
Try to find some vanilla Minecraft cows if at all possible. There are many cows from the Animania mod, but they are harder to care for, requiring food and water. Vanilla cows don't need either of these things, and you can right-click them with an empty bucket in hand to get Milk, which you can drink to increase your Dairy bar. If you want to bring a cow to your base, lure it that way with wheat, or simply craft a piggybackpack, equip it as your chestplate and right click on a cow to carry it. Once you have your cow in an enclosed area, simply remove the piggybackpack to drop the cow. (Cow in a Jar is also an easy way to passively get milk, but it still requires a vanilla Cow).
Vegetables[]
Raw Pam's Harvestcraft vegetables can be acquired from various "garden" plants scattered across the world. These vegetables can be placed in a crafting table to create seeds, which can be planted in soil tilled by a Mattock. The raw vegetables are mediocre at best, but a they will increase your bar a bit. Vanilla potatoes can also be found from certain types of gardens, and they can be cooked into baked potatoes, which are quite a good food source
Grain[]
Vanilla bread is not that easy to come by in this modpack. A good substitute to fill your grain bar with is baguettes. Baguettes are crafted by smelting dough (crafted with 2 wheat), and fill your Grain and hunger bars by quite a bit.
Fruit[]
Fruit is very easy to gather and find. Apples make a great food source, since they restore quite a bit of hunger. If possible, gather 3 apples, either by cutting down oak trees, or right-clicking ripe apples from apple trees, and create an apple sapling in a crafting table. Plant this sapling near your base, and you'll have an no-hassle, renewable source of apples.