Learn Italian: Mi piace disegnare i miei gatti.

With the verb piacere, the thing you like is the subject. Here, the thing you like is the action of drawing (disegnare). Whenever you say you like doing an action (using an infinitive verb), you always use the singular piace, even if a plural word like i miei gatti comes later in the sentence.

What does the mi mean at the start of the sentence?

Mi means "to me". In Italian, you don't actually say "I like". The verb piacere means "to be pleasing". So, Mi piace disegnare literally translates to "To draw is pleasing to me."

Why do we need the word i in i miei gatti? Doesn't that mean "the my cats"?

Yes, it does! In Italian, possessive words like miei (my) almost always need a definite article right in front of them. Since gatti is a masculine plural noun, we must use the masculine plural article i.

I see disegnare looks like the English word "design". Does it mean that too?

It is a "false friend"! While they look similar, disegnare specifically means "to draw" or "to sketch" with a pen or pencil. If you want to talk about designing something, Italians usually use a different verb, like progettare.